/*============================================================================
 * Convection-diffusion operators.
 *============================================================================*/

/*
  This file is part of Code_Saturne, a general-purpose CFD tool.

  Copyright (C) 1998-2020 EDF S.A.

  This program is free software; you can redistribute it and/or modify it under
  the terms of the GNU General Public License as published by the Free Software
  Foundation; either version 2 of the License, or (at your option) any later
  version.

  This program is distributed in the hope that it will be useful, but WITHOUT
  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
  details.

  You should have received a copy of the GNU General Public License along with
  this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
  Street, Fifth Floor, Boston, MA 02110-1301, USA. */

/*----------------------------------------------------------------------------*/

#include "cs_defs.h"

/*----------------------------------------------------------------------------
 * Standard C library headers
 *----------------------------------------------------------------------------*/

#include <assert.h>
#include <errno.h>
#include <stdio.h>
#include <stdarg.h>
#include <string.h>
#include <math.h>
#include <float.h>

#if defined(HAVE_MPI)
#include <mpi.h>
#endif

/*----------------------------------------------------------------------------
 *  Local headers
 *----------------------------------------------------------------------------*/

#include "bft_error.h"
#include "bft_mem.h"
#include "bft_printf.h"

#include "cs_blas.h"
#include "cs_halo.h"
#include "cs_halo_perio.h"
#include "cs_log.h"
#include "cs_math.h"
#include "cs_mesh.h"
#include "cs_field.h"
#include "cs_field_operator.h"
#include "cs_field_pointer.h"
#include "cs_gradient.h"
#include "cs_gradient_perio.h"
#include "cs_ext_neighborhood.h"
#include "cs_mesh_quantities.h"
#include "cs_parall.h"
#include "cs_parameters.h"
#include "cs_porous_model.h"
#include "cs_prototypes.h"
#include "cs_timer.h"
#include "cs_stokes_model.h"
#include "cs_boundary_conditions.h"
#include "cs_internal_coupling.h"
#include "cs_bad_cells_regularisation.h"

/*----------------------------------------------------------------------------
 *  Header for the current file
 *----------------------------------------------------------------------------*/

#include "cs_convection_diffusion.h"

/*----------------------------------------------------------------------------*/

BEGIN_C_DECLS

/*=============================================================================
 * Additional Doxygen documentation
 *============================================================================*/

/*! \file  cs_convection_diffusion.c
 *
 * \brief Convection-diffusion operators.
 *
 * Please refer to the
 * <a href="../../theory.pdf#conv-diff"><b>convection-diffusion</b></a> section
 *  of the theory guide for more informations.
 */
/*! \cond DOXYGEN_SHOULD_SKIP_THIS */

/*=============================================================================
 * Local Macro Definitions
 *============================================================================*/

/*=============================================================================
 * Local type definitions
 *============================================================================*/

/*============================================================================
 * Private function definitions
 *============================================================================*/

/*----------------------------------------------------------------------------
 * Return the denominator to build the beta blending coefficient of the
 * beta limiter (ensuring preservation of a given min/max pair of values).
 *
 * parameters:
 *   f_id        <-- field id (or -1)
 *   inc         <-- 0 if an increment, 1 otherwise
 *   denom_inf   --> computed denominator for the inferior bound
 *   denom_sup   --> computed denominator for the superior bound
 *
 * return:
 *   pointer to local values array, or NULL;
 *----------------------------------------------------------------------------*/

static void
_beta_limiter_denom(const int              f_id,
                    const int              inc,
                    cs_real_t    *restrict denom_inf,
                    cs_real_t    *restrict denom_sup)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;

  /* Get option from the field */
  cs_field_t *f = cs_field_by_id(f_id);

  const cs_real_t *restrict pvar  = f->val;
  const cs_real_t *restrict pvara = f->val_pre;

  const cs_real_t *restrict coefap = f->bc_coeffs->a;
  const cs_real_t *restrict coefbp = f->bc_coeffs->b;

  int key_cal_opt_id = cs_field_key_id("var_cal_opt");
  cs_var_cal_opt_t var_cal_opt;

  cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);

  const int ischcp = var_cal_opt.ischcv;
  const int ircflp = var_cal_opt.ircflu;
  const int imrgra = var_cal_opt.imrgra;
  const cs_real_t thetap = var_cal_opt.thetav;
  const cs_real_t blencp = var_cal_opt.blencv;

  const int kimasf = cs_field_key_id("inner_mass_flux_id");
  const int kbmasf = cs_field_key_id("boundary_mass_flux_id");
  const cs_real_t *restrict i_massflux =
    cs_field_by_id(cs_field_get_key_int(f, kimasf))->val;
  const cs_real_t *restrict b_massflux =
    cs_field_by_id(cs_field_get_key_int(f, kbmasf))->val;

  /* select halo type according to field gradient method */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* for NVD / TVD schemes (including VoF schemes) */

  const int key_lim_choice = cs_field_key_id("limiter_choice");
  int limiter_choice = -1;

  cs_real_t *local_min = NULL;
  cs_real_t *local_max = NULL;
  cs_real_t *courant = NULL;

  if (ischcp == 4) {
    /* get limiter choice */
    limiter_choice = cs_field_get_key_int(f, key_lim_choice);

    /* local extrema computation */
    BFT_MALLOC(local_max, n_cells_ext, cs_real_t);
    BFT_MALLOC(local_min, n_cells_ext, cs_real_t);
    cs_field_local_extrema_scalar(f_id,
                                  halo_type,
                                  local_max,
                                  local_min);

    /* cell Courant number computation */
    if (limiter_choice >= CS_NVD_VOF_HRIC) {
      BFT_MALLOC(courant, n_cells_ext, cs_real_t);
      cs_cell_courant_number(f_id, courant);
    }
  }

  cs_real_t *df_limiter = NULL;
  int df_limiter_id =
    cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
  if (df_limiter_id > -1)
    df_limiter = cs_field_by_id(df_limiter_id)->val;

  /* step 1: gradient computation */
  cs_real_3_t *grdpa;  /* for the implicit part */
  cs_real_3_t *grdpaa; /* for the explicit part */

  BFT_MALLOC(grdpa, n_cells_ext, cs_real_3_t);
  BFT_MALLOC(grdpaa, n_cells_ext, cs_real_3_t);

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
    grdpa[cell_id][0] = 0.;
    grdpa[cell_id][1] = 0.;
    grdpa[cell_id][2] = 0.;

    grdpaa[cell_id][0] = 0.;
    grdpaa[cell_id][1] = 0.;
    grdpaa[cell_id][2] = 0.;
  }

  /* legacy SOLU Scheme or centered scheme */
  if (ischcp == 0 || ischcp == 1 || ischcp == 3) {

    cs_field_gradient_scalar(f,
                             false, /* use_previous_t */
                             inc,
                             true, /* _recompute_cocg */
                             grdpa);

    cs_field_gradient_scalar(f,
                             true, /* use_previous_t */
                             inc,
                             true, /* _recompute_cocg */
                             grdpaa);

  }
  /* pure SOLU scheme (upwind gradient reconstruction) */
  else if (ischcp == 2) {

    cs_upwind_gradient(f_id,
                       inc,
                       halo_type,
                       coefap,
                       coefbp,
                       i_massflux,
                       b_massflux,
                       pvar,
                       grdpa);

    cs_upwind_gradient(f_id,
                       inc,
                       halo_type,
                       coefap,
                       coefbp,
                       i_massflux,
                       b_massflux,
                       pvara,
                       grdpaa);

  }

  /* Step 2: Building of denominator */

# pragma omp parallel for
  for (cs_lnum_t ii = 0; ii < n_cells_ext; ii++) {
    denom_inf[ii] = 0.;
    denom_sup[ii] = 0.;
  }

  /* ---> Contribution from interior faces */

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
          face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
          face_id++) {

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        cs_real_t pi = pvar[ii];
        cs_real_t pj = pvar[jj];
        cs_real_t pia = pvara[ii];
        cs_real_t pja = pvara[jj];
        cs_real_t pif, pjf, pip, pjp;
        cs_real_t pifa, pjfa, pipa, pjpa;

        cs_real_t hybrid_coef_ii, hybrid_coef_jj;
        if (ischcp == 3) {
          hybrid_coef_ii = CS_F_(hybrid_blend)->val[ii];
          hybrid_coef_jj = CS_F_(hybrid_blend)->val[jj];
        } else {
          hybrid_coef_ii = 0.;
          hybrid_coef_jj = 0.;
        }

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

        if (ischcp == 4) {
          /* NVD/TVD family of high accuracy schemes */

          cs_lnum_t ic, id;

          /* Determine central and downwind sides w.r.t. current face */
          cs_central_downwind_cells(ii,
                                    jj,
                                    i_massflux[face_id],
                                    &ic,  /* central cell id */
                                    &id); /* downwind cell id */

          cs_real_t courant_c = -1.;
          if (courant != NULL)
            courant_c = courant[ic];

          cs_i_cd_unsteady_nvd(limiter_choice,
                               blencp,
                               cell_cen[ic],
                               cell_cen[id],
                               i_face_normal[face_id],
                               i_face_cog[face_id],
                               grdpa[ic],
                               pvar[ic],
                               pvar[id],
                               local_max[ic],
                               local_min[ic],
                               courant_c,
                               &pif,
                               &pjf);

          cs_i_cd_unsteady_nvd(limiter_choice,
                               blencp,
                               cell_cen[ic],
                               cell_cen[id],
                               i_face_normal[face_id],
                               i_face_cog[face_id],
                               grdpaa[ic],
                               pvara[ic],
                               pvara[id],
                               local_max[ic],
                               local_min[ic],
                               courant_c,
                               &pifa,
                               &pjfa);
        } else {
          /* Value at time n */
          cs_i_cd_unsteady(bldfrp,
                           ischcp,
                           blencp,
                           weight[face_id],
                           cell_cen[ii],
                           cell_cen[jj],
                           i_face_cog[face_id],
                           hybrid_coef_ii,
                           hybrid_coef_jj,
                           diipf[face_id],
                           djjpf[face_id],
                           grdpa[ii], /* Std gradient when needed */
                           grdpa[jj], /* Std gradient when needed */
                           grdpa[ii], /* Upwind gradient when needed */
                           grdpa[jj], /* Upwind gradient when needed */
                           pi,
                           pj,
                           &pif,
                           &pjf,
                           &pip,
                           &pjp);

          /* Value at time n-1 */
          cs_i_cd_unsteady(bldfrp,
                           ischcp,
                           blencp,
                           weight[face_id],
                           cell_cen[ii],
                           cell_cen[jj],
                           i_face_cog[face_id],
                           hybrid_coef_ii, /* FIXME use previous values
                                              of blending function */
                           hybrid_coef_jj, /* FIXME use previous values
                                              of blending function */
                           diipf[face_id],
                           djjpf[face_id],
                           grdpaa[ii], /* Std gradient when needed */
                           grdpaa[jj], /* Std gradient when needed */
                           grdpaa[ii], /* Upwind gradient when needed */
                           grdpaa[jj], /* Upwind gradient when needed */
                           pia,
                           pja,
                           &pifa,
                           &pjfa,
                           &pipa,
                           &pjpa);
        }

        cs_real_t flui = 0.5*(i_massflux[face_id] +fabs(i_massflux[face_id]));
        cs_real_t fluj = 0.5*(i_massflux[face_id] -fabs(i_massflux[face_id]));

        cs_real_t flux =     thetap  * ( (pif  - pi )*flui
                                       + (pjf  - pj )*fluj)
                       + (1.-thetap) * ( (pifa - pia)*flui
                                       + (pjfa - pja)*fluj);

        /* blending to prevent INFERIOR bound violation
          We need to take the positive part*/
        cs_real_t partii = 0.5*(flux + CS_ABS(flux));
        cs_real_t partjj = 0.5*(flux - CS_ABS(flux));

        denom_inf[ii] = denom_inf[ii] + partii;
        denom_inf[jj] = denom_inf[jj] - partjj;

        /* blending to prevent SUPERIOR bound violation
          We need to take the negative part
          Note: the swap between ii and jj is due to the fact
          that an upwind value on (Y-bound) is equivalent to a
          downwind value on (bound-Y) */
        denom_sup[ii] = denom_sup[ii] - partjj;
        denom_sup[jj] = denom_sup[jj] + partii;
      }
    }
  }

  //Free Gradient arrays
  BFT_FREE(local_min);
  BFT_FREE(local_max);
  BFT_FREE(courant);
  BFT_FREE(grdpa);
  BFT_FREE(grdpaa);

}

/*----------------------------------------------------------------------------
 * Return the diagonal part of the numerator to build the Min/max limiter.
 *
 * parameters:
 *   f_id        <-- field id (or -1)
 *   rovsdt      <-- rho * volume / dt
 *   num_inf     --> computed numerator for the inferior bound
 *   num_sup     --> computed numerator for the superior bound
 *
 *----------------------------------------------------------------------------*/

static void
_beta_limiter_num(const int           f_id,
                  const int           inc,
                  const cs_real_t     rovsdt[],
                  cs_real_t          *num_inf,
                  cs_real_t          *num_sup)
{
  const cs_mesh_t  *m = cs_glob_mesh;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;

  /* Get option from the field */
  cs_field_t *f = cs_field_by_id(f_id);

  const cs_real_t *restrict pvara = f->val_pre;

  const cs_real_t *restrict coefap = f->bc_coeffs->a;
  const cs_real_t *restrict coefbp = f->bc_coeffs->b;

  int key_scamax_id = cs_field_key_id("max_scalar");
  int key_scamin_id = cs_field_key_id("min_scalar");

  cs_real_t scalar_max = cs_field_get_key_double(f, key_scamax_id);
  cs_real_t scalar_min = cs_field_get_key_double(f, key_scamin_id);

  int key_cal_opt_id = cs_field_key_id("var_cal_opt");
  cs_var_cal_opt_t var_cal_opt;

  cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);

  const cs_real_t thetex =  1.-var_cal_opt.thetav;

  const int kimasf = cs_field_key_id("inner_mass_flux_id");
  const int kbmasf = cs_field_key_id("boundary_mass_flux_id");
  const cs_real_t *restrict i_massflux =
    cs_field_by_id( cs_field_get_key_int(f, kimasf) )->val;
  const cs_real_t *restrict b_massflux =
    cs_field_by_id( cs_field_get_key_int(f, kbmasf) )->val;

  for (cs_lnum_t ii = n_cells; ii < n_cells_ext; ii++) {
    num_inf[ii] = 0.;
    num_sup[ii] = 0.;
  }

# pragma omp parallel for
  for (cs_lnum_t ii = 0; ii < n_cells; ii++) {
    num_inf[ii] = rovsdt[ii] * (pvara[ii] -scalar_min);
    num_sup[ii] = rovsdt[ii] * (scalar_max-pvara[ii]);
  }

  /* ---> Contribution from interior faces */

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
          face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
          face_id++) {

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        cs_real_t flui = 0.5*(i_massflux[face_id] + fabs(i_massflux[face_id]));
        cs_real_t fluj = 0.5*(i_massflux[face_id] - fabs(i_massflux[face_id]));

        cs_real_t pi = pvara[ii]-scalar_min;
        cs_real_t pj = pvara[jj]-scalar_min;

        num_inf[ii] -= thetex *(pi * flui + pj * fluj);
        num_inf[jj] += thetex *(pj * fluj + pi * flui);

        pi = scalar_max-pvara[ii];
        pj = scalar_max-pvara[jj];

        num_sup[ii] -= thetex *(pi * flui + pj * fluj);
        num_sup[jj] += thetex *(pj * fluj + pi * flui);
      }
    }
  }

  /* ---> Contribution from boundary faces */

  for (int g_id = 0; g_id < n_b_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_b_threads; t_id++) {
      for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
          face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
          face_id++) {

        cs_lnum_t ii = b_face_cells[face_id];

        cs_real_t flui = 0.5*(b_massflux[face_id]+fabs(b_massflux[face_id]));
        cs_real_t fluf = 0.5*(b_massflux[face_id]-fabs(b_massflux[face_id]));
        cs_real_t pfabor = inc*coefap[face_id]+coefbp[face_id]*pvara[ii];

        num_inf[ii] -= thetex *( (pvara[ii]-scalar_min) * flui
                               + (pfabor   -scalar_min) * fluf);
        num_sup[ii] -= thetex *( (scalar_max-pvara[ii]) * flui
                               + (scalar_max-pfabor   ) * fluf);
      }
    }
  }
}

/*! (DOXYGEN_SHOULD_SKIP_THIS) \endcond */

/*============================================================================
 * Public function definitions for Fortran API
 *============================================================================*/

/*----------------------------------------------------------------------------
 * Wrapper to cs_face_diffusion_potential
 *----------------------------------------------------------------------------*/

void CS_PROCF (itrmas, ITRMAS)
(
 const int       *const   f_id,
 const int       *const   init,
 const int       *const   inc,
 const int       *const   imrgra,
 const int       *const   iccocg,
 const int       *const   nswrgp,
 const int       *const   imligp,
 const int       *const   iphydp,
 const int       *const   iwgrp,
 const int       *const   iwarnp,
 const cs_real_t *const   epsrgp,
 const cs_real_t *const   climgp,
 const cs_real_t *const   extrap,
 cs_real_3_t              frcxt[],
 cs_real_t                pvar[],
 const cs_real_t          coefap[],
 const cs_real_t          coefbp[],
 const cs_real_t          cofafp[],
 const cs_real_t          cofbfp[],
 const cs_real_t          i_visc[],
 const cs_real_t          b_visc[],
 cs_real_t                visel[],
 cs_real_t                i_massflux[],
 cs_real_t                b_massflux[]
)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  cs_face_diffusion_potential(*f_id,
                              m,
                              fvq,
                              *init,
                              *inc,
                              *imrgra,
                              *iccocg,
                              *nswrgp,
                              *imligp,
                              *iphydp,
                              *iwgrp,
                              *iwarnp,
                              *epsrgp,
                              *climgp,
                              frcxt,
                              pvar,
                              coefap,
                              coefbp,
                              cofafp,
                              cofbfp,
                              i_visc,
                              b_visc,
                              visel,
                              i_massflux,
                              b_massflux);
}

/*----------------------------------------------------------------------------
 * Wrapper to cs_face_anisotropic_diffusion_potential
 *----------------------------------------------------------------------------*/

void CS_PROCF (itrmav, ITRMAV)
(
 const int       *const   f_id,
 const int       *const   init,
 const int       *const   inc,
 const int       *const   imrgra,
 const int       *const   iccocg,
 const int       *const   nswrgp,
 const int       *const   imligp,
 const int       *const   ircflp,
 const int       *const   iphydp,
 const int       *const   iwgrp,
 const int       *const   iwarnp,
 const cs_real_t *const   epsrgp,
 const cs_real_t *const   climgp,
 const cs_real_t *const   extrap,
 cs_real_3_t              frcxt[],
 cs_real_t                pvar[],
 const cs_real_t          coefap[],
 const cs_real_t          coefbp[],
 const cs_real_t          cofafp[],
 const cs_real_t          cofbfp[],
 const cs_real_t          i_visc[],
 const cs_real_t          b_visc[],
 cs_real_6_t              viscel[],
 const cs_real_2_t        weighf[],
 const cs_real_t          weighb[],
 cs_real_t                i_massflux[],
 cs_real_t                b_massflux[]
)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  cs_face_anisotropic_diffusion_potential(*f_id,
                                          m,
                                          fvq,
                                          *init,
                                          *inc,
                                          *imrgra,
                                          *iccocg,
                                          *nswrgp,
                                          *imligp,
                                          *ircflp,
                                          *iphydp,
                                          *iwgrp,
                                          *iwarnp,
                                          *epsrgp,
                                          *climgp,
                                          frcxt,
                                          pvar,
                                          coefap,
                                          coefbp,
                                          cofafp,
                                          cofbfp,
                                          i_visc,
                                          b_visc,
                                          viscel,
                                          weighf,
                                          weighb,
                                          i_massflux,
                                          b_massflux);
}

/*----------------------------------------------------------------------------
 * Wrapper to cs_diffusion_potential
 *----------------------------------------------------------------------------*/

void CS_PROCF (itrgrp, ITRGRP)
(
 const int       *const   f_id,
 const int       *const   init,
 const int       *const   inc,
 const int       *const   imrgra,
 const int       *const   iccocg,
 const int       *const   nswrgp,
 const int       *const   imligp,
 const int       *const   iphydp,
 const int       *const   iwgrp,
 const int       *const   iwarnp,
 const cs_real_t *const   epsrgp,
 const cs_real_t *const   climgp,
 const cs_real_t *const   extrap,
 cs_real_3_t              frcxt[],
 cs_real_t                pvar[],
 const cs_real_t          coefap[],
 const cs_real_t          coefbp[],
 const cs_real_t          cofafp[],
 const cs_real_t          cofbfp[],
 const cs_real_t          i_visc[],
 const cs_real_t          b_visc[],
 cs_real_t                visel[],
 cs_real_t                diverg[]
)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  cs_diffusion_potential(*f_id,
                         m,
                         fvq,
                         *init,
                         *inc,
                         *imrgra,
                         *iccocg,
                         *nswrgp,
                         *imligp,
                         *iphydp,
                         *iwgrp,
                         *iwarnp,
                         *epsrgp,
                         *climgp,
                         frcxt,
                         pvar,
                         coefap,
                         coefbp,
                         cofafp,
                         cofbfp,
                         i_visc,
                         b_visc,
                         visel,
                         diverg);
}

/*----------------------------------------------------------------------------
 * Wrapper to cs_anisotropic_diffusion_potential
 *----------------------------------------------------------------------------*/

void CS_PROCF (itrgrv, ITRGRV)
(
 const int       *const   f_id,
 const int       *const   init,
 const int       *const   inc,
 const int       *const   imrgra,
 const int       *const   iccocg,
 const int       *const   nswrgp,
 const int       *const   imligp,
 const int       *const   ircflp,
 const int       *const   iphydp,
 const int       *const   iwgrp,
 const int       *const   iwarnp,
 const cs_real_t *const   epsrgp,
 const cs_real_t *const   climgp,
 const cs_real_t *const   extrap,
 cs_real_3_t              frcxt[],
 cs_real_t                pvar[],
 const cs_real_t          coefap[],
 const cs_real_t          coefbp[],
 const cs_real_t          cofafp[],
 const cs_real_t          cofbfp[],
 const cs_real_t          i_visc[],
 const cs_real_t          b_visc[],
 cs_real_6_t              viscel[],
 const cs_real_2_t        weighf[],
 const cs_real_t          weighb[],
 cs_real_t                diverg[]
)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  cs_anisotropic_diffusion_potential(*f_id,
                                     m,
                                     fvq,
                                     *init,
                                     *inc,
                                     *imrgra,
                                     *iccocg,
                                     *nswrgp,
                                     *imligp,
                                     *ircflp,
                                     *iphydp,
                                     *iwgrp,
                                     *iwarnp,
                                     *epsrgp,
                                     *climgp,
                                     frcxt,
                                     pvar,
                                     coefap,
                                     coefbp,
                                     cofafp,
                                     cofbfp,
                                     i_visc,
                                     b_visc,
                                     viscel,
                                     weighf,
                                     weighb,
                                     diverg);
}

/*============================================================================
 * Public function definitions
 *============================================================================*/

/*----------------------------------------------------------------------------*/
/*!
 * \brief Compute the upwind gradient used in the slope tests.
 *
 * This function assumes the input gradient and pvar values have already
 * been synchronized.
 *
 * \param[in]     f_id         field id
 * \param[in]     inc          Not an increment flag
 * \param[in]     halo_type    halo type
 * \param[in]     grad         standard gradient
 * \param[out]    grdpa        upwind gradient
 * \param[in]     pvar         values
 * \param[in]     coefap       boundary condition array for the variable
 *                             (explicit part)
 * \param[in]     coefbp       boundary condition array for the variable
 *                             (implicit part)
 * \param[in]     i_massflux   mass flux at interior faces
 */
/*----------------------------------------------------------------------------*/

void
cs_slope_test_gradient(int                     f_id,
                       int                     inc,
                       cs_halo_type_t          halo_type,
                       const cs_real_3_t      *grad,
                       cs_real_3_t            *grdpa,
                       const cs_real_t        *pvar,
                       const cs_real_t        *coefap,
                       const cs_real_t        *coefbp,
                       const cs_real_t        *i_massflux)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        cs_real_t difx = i_face_cog[face_id][0] - cell_cen[ii][0];
        cs_real_t dify = i_face_cog[face_id][1] - cell_cen[ii][1];
        cs_real_t difz = i_face_cog[face_id][2] - cell_cen[ii][2];
        cs_real_t djfx = i_face_cog[face_id][0] - cell_cen[jj][0];
        cs_real_t djfy = i_face_cog[face_id][1] - cell_cen[jj][1];
        cs_real_t djfz = i_face_cog[face_id][2] - cell_cen[jj][2];

        cs_real_t pif =   pvar[ii]
                        + difx*grad[ii][0]+dify*grad[ii][1]+difz*grad[ii][2];
        cs_real_t pjf =   pvar[jj]
                        + djfx*grad[jj][0]+djfy*grad[jj][1]+djfz*grad[jj][2];

        cs_real_t pfac = pjf;
        if (i_massflux[face_id] > 0.) pfac = pif;

        cs_real_t pfac1 = pfac*i_face_normal[face_id][0];
        cs_real_t pfac2 = pfac*i_face_normal[face_id][1];
        cs_real_t pfac3 = pfac*i_face_normal[face_id][2];

        grdpa[ii][0] = grdpa[ii][0] + pfac1;
        grdpa[ii][1] = grdpa[ii][1] + pfac2;
        grdpa[ii][2] = grdpa[ii][2] + pfac3;

        grdpa[jj][0] = grdpa[jj][0] - pfac1;
        grdpa[jj][1] = grdpa[jj][1] - pfac2;
        grdpa[jj][2] = grdpa[jj][2] - pfac3;

      }
    }
  }

  for (int g_id = 0; g_id < n_b_groups; g_id++) {
#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (int t_id = 0; t_id < n_b_threads; t_id++) {
      for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        cs_lnum_t ii = b_face_cells[face_id];

        cs_real_t pfac = inc*coefap[face_id] + coefbp[face_id]
          * (pvar[ii] + cs_math_3_dot_product(grad[ii], diipb[face_id]));
        grdpa[ii][0] = grdpa[ii][0] + pfac*b_face_normal[face_id][0];
        grdpa[ii][1] = grdpa[ii][1] + pfac*b_face_normal[face_id][1];
        grdpa[ii][2] = grdpa[ii][2] + pfac*b_face_normal[face_id][2];

      }
    }
  }

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {

    cs_real_t unsvol = 1./cell_vol[cell_id];

    grdpa[cell_id][0] = grdpa[cell_id][0]*unsvol;
    grdpa[cell_id][1] = grdpa[cell_id][1]*unsvol;
    grdpa[cell_id][2] = grdpa[cell_id][2]*unsvol;

  }

  /* Synchronization for parallelism or periodicity */

  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)grdpa, 3);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_vect(halo, CS_HALO_STANDARD, (cs_real_t *)grdpa, 3);

    /* Gradient periodicity of rotation for Reynolds stress components */
    if (cs_glob_mesh->have_rotation_perio > 0 && f_id != -1)
      cs_gradient_perio_process_rij(f_id, grdpa);
  }

}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Compute the upwind gradient used in the pure SOLU schemes
 *        (observed in the litterature).
 *
 * \param[in]     f_id         field index
 * \param[in]     inc          Not an increment flag
 * \param[in]     halo_type    halo type
 * \param[in]     coefap       boundary condition array for the variable
 *                             (explicit part)
 * \param[in]     coefbp       boundary condition array for the variable
 *                             (implicit part)
 * \param[in]     i_massflux   mass flux at interior faces
 * \param[in]     b_massflux   mass flux at boundary faces
 * \param[in]     pvar         values
 * \param[out]    grdpa        upwind gradient
 */
/*----------------------------------------------------------------------------*/

void
cs_upwind_gradient(const int                     f_id,
                   const int                     inc,
                   const cs_halo_type_t          halo_type,
                   const cs_real_t               coefap[],
                   const cs_real_t               coefbp[],
                   const cs_real_t               i_massflux[],
                   const cs_real_t               b_massflux[],
                   const cs_real_t     *restrict pvar,
                   cs_real_3_t         *restrict grdpa)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        cs_real_t pif = pvar[ii];
        cs_real_t pjf = pvar[jj];

        cs_real_t pfac = pjf;
        if (i_massflux[face_id] > 0.) pfac = pif;

        cs_real_t pfac1 = pfac*i_face_normal[face_id][0];
        cs_real_t pfac2 = pfac*i_face_normal[face_id][1];
        cs_real_t pfac3 = pfac*i_face_normal[face_id][2];

        grdpa[ii][0] = grdpa[ii][0] + pfac1;
        grdpa[ii][1] = grdpa[ii][1] + pfac2;
        grdpa[ii][2] = grdpa[ii][2] + pfac3;

        grdpa[jj][0] = grdpa[jj][0] - pfac1;
        grdpa[jj][1] = grdpa[jj][1] - pfac2;
        grdpa[jj][2] = grdpa[jj][2] - pfac3;

      }
    }
  }

  for (int g_id = 0; g_id < n_b_groups; g_id++) {
#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (int t_id = 0; t_id < n_b_threads; t_id++) {
      for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        cs_lnum_t ii = b_face_cells[face_id];

        cs_real_t pfac = pvar[ii];

        if (b_massflux[face_id] < 0)
          pfac = inc*coefap[face_id] + coefbp[face_id] * pvar[ii];

        grdpa[ii][0] = grdpa[ii][0] + pfac*b_face_normal[face_id][0];
        grdpa[ii][1] = grdpa[ii][1] + pfac*b_face_normal[face_id][1];
        grdpa[ii][2] = grdpa[ii][2] + pfac*b_face_normal[face_id][2];

      }
    }
  }

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {

    cs_real_t unsvol = 1./cell_vol[cell_id];

    grdpa[cell_id][0] = grdpa[cell_id][0]*unsvol;
    grdpa[cell_id][1] = grdpa[cell_id][1]*unsvol;
    grdpa[cell_id][2] = grdpa[cell_id][2]*unsvol;

  }

  /* Synchronization for parallelism or periodicity */

  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)grdpa, 3);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_vect(halo, halo_type, (cs_real_t *)grdpa, 3);

    /* Gradient periodicity of rotation for Reynolds stress components */
    if (cs_glob_mesh->have_rotation_perio > 0 && f_id != -1)
      cs_gradient_perio_process_rij(f_id, grdpa);
  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Compute the upwind gradient used in the slope tests.
 *
 * This function assumes the input gradient and pvar values have already
 * been synchronized.
 *
 * \param[in]     inc          Not an increment flag
 * \param[in]     halo_type    halo type
 * \param[in]     grad         standard gradient
 * \param[out]    grdpa        upwind gradient
 * \param[in]     pvar         values
 * \param[in]     coefa        boundary condition array for the variable
                               (Explicit part)
 * \param[in]     coefb        boundary condition array for the variable
                              (Implicit part)
 * \param[in]     i_massflux   mass flux at interior faces
 */
/*----------------------------------------------------------------------------*/

void
cs_slope_test_gradient_vector(const int              inc,
                              const cs_halo_type_t   halo_type,
                              const cs_real_33_t    *grad,
                              cs_real_33_t          *grdpa,
                              const cs_real_3_t     *pvar,
                              const cs_real_3_t     *coefa,
                              const cs_real_33_t    *coefb,
                              const cs_real_t       *i_massflux)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_f_face_normal
    = (const cs_real_3_t *restrict)fvq->i_f_face_normal;
  const cs_real_3_t *restrict b_f_face_normal
    = (const cs_real_3_t *restrict)fvq->b_f_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        cs_real_t difv[3], djfv[3];

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        for (int jsou = 0; jsou < 3; jsou++) {
          difv[jsou] = i_face_cog[face_id][jsou] - cell_cen[ii][jsou];
          djfv[jsou] = i_face_cog[face_id][jsou] - cell_cen[jj][jsou];
        }

        /* x-y-z component, p = u, v, w */

        for (int isou = 0; isou < 3; isou++) {
          cs_real_t pif = pvar[ii][isou];
          cs_real_t pjf = pvar[jj][isou];
          for (int jsou = 0; jsou < 3; jsou++) {
            pif = pif + grad[ii][isou][jsou]*difv[jsou];
            pjf = pjf + grad[jj][isou][jsou]*djfv[jsou];
          }

          cs_real_t pfac = pjf;
          if (i_massflux[face_id] > 0.) pfac = pif;

          /* U gradient */

          cs_real_t vfac[3];

          for (int jsou = 0; jsou < 3; jsou++) {
            vfac[jsou] = pfac*i_f_face_normal[face_id][jsou];

            grdpa[ii][isou][jsou] = grdpa[ii][isou][jsou] + vfac[jsou];
            grdpa[jj][isou][jsou] = grdpa[jj][isou][jsou] - vfac[jsou];
          }
        }

      }
    }
  }

  for (int g_id = 0; g_id < n_b_groups; g_id++) {
#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (int t_id = 0; t_id < n_b_threads; t_id++) {
      for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        cs_real_t diipbv[3];
        cs_lnum_t ii = b_face_cells[face_id];

        for (int jsou = 0; jsou < 3; jsou++)
          diipbv[jsou] = diipb[face_id][jsou];

        /* x-y-z components, p = u, v, w */

        for (int isou = 0; isou < 3; isou++) {
          cs_real_t pfac = inc*coefa[face_id][isou];
          /*coefu is a matrix */
          for (int jsou =  0; jsou < 3; jsou++)
            pfac += coefb[face_id][jsou][isou]*(  pvar[ii][jsou]
                                                + grad[ii][jsou][0]*diipbv[0]
                                                + grad[ii][jsou][1]*diipbv[1]
                                                + grad[ii][jsou][2]*diipbv[2]);

          for (int jsou = 0; jsou < 3; jsou++)
            grdpa[ii][isou][jsou] += pfac*b_f_face_normal[face_id][jsou];
        }

      }
    }
  }

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
    cs_real_t unsvol = 1./cell_vol[cell_id];
    for (int isou = 0; isou < 3; isou++) {
      for (int jsou = 0; jsou < 3; jsou++)
        grdpa[cell_id][isou][jsou] = grdpa[cell_id][isou][jsou]*unsvol;
    }
  }

  /* Handle parallelism and periodicity */

  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)grdpa, 9);
    if (m->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(halo, halo_type, (cs_real_t *)grdpa);
  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Compute the upwind gradient used in the slope tests.
 *
 * This function assumes the input gradient and pvar values have already
 * been synchronized.
 *
 * \param[in]     inc          Not an increment flag
 * \param[in]     halo_type    halo type
 * \param[in]     grad         standard gradient
 * \param[out]    grdpa        upwind gradient
 * \param[in]     pvar         values
 * \param[in]     coefa        boundary condition array for the variable
                               (Explicit part)
 * \param[in]     coefb        boundary condition array for the variable
                              (Implicit part)
 * \param[in]     i_massflux   mass flux at interior faces
 */
/*----------------------------------------------------------------------------*/

void
cs_slope_test_gradient_tensor(const int              inc,
                              const cs_halo_type_t   halo_type,
                              const cs_real_63_t    *grad,
                              cs_real_63_t          *grdpa,
                              const cs_real_6_t     *pvar,
                              const cs_real_6_t     *coefa,
                              const cs_real_66_t    *coefb,
                              const cs_real_t       *i_massflux)
{
  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_f_face_normal
    = (const cs_real_3_t *restrict)fvq->i_f_face_normal;
  const cs_real_3_t *restrict b_f_face_normal
    = (const cs_real_3_t *restrict)fvq->b_f_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  for (int g_id = 0; g_id < n_i_groups; g_id++) {
#   pragma omp parallel for
    for (int t_id = 0; t_id < n_i_threads; t_id++) {
      for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
           face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
           face_id++) {

        cs_real_t difv[3], djfv[3];

        cs_lnum_t ii = i_face_cells[face_id][0];
        cs_lnum_t jj = i_face_cells[face_id][1];

        for (int jsou = 0; jsou < 3; jsou++) {
          difv[jsou] = i_face_cog[face_id][jsou] - cell_cen[ii][jsou];
          djfv[jsou] = i_face_cog[face_id][jsou] - cell_cen[jj][jsou];
        }

        /* x-y-z component, p = u, v, w */

        for (int isou = 0; isou < 6; isou++) {
          cs_real_t pif = pvar[ii][isou];
          cs_real_t pjf = pvar[jj][isou];
          for (int jsou = 0; jsou < 3; jsou++) {
            pif = pif + grad[ii][isou][jsou]*difv[jsou];
            pjf = pjf + grad[jj][isou][jsou]*djfv[jsou];
          }

          cs_real_t pfac = pjf;
          if (i_massflux[face_id] > 0.) pfac = pif;

          /* U gradient */

          cs_real_t vfac[3];

          for (int jsou = 0; jsou < 3; jsou++) {
            vfac[jsou] = pfac*i_f_face_normal[face_id][jsou];

            grdpa[ii][isou][jsou] = grdpa[ii][isou][jsou] + vfac[jsou];
            grdpa[jj][isou][jsou] = grdpa[jj][isou][jsou] - vfac[jsou];
          }
        }

      }
    }
  }

  for (int g_id = 0; g_id < n_b_groups; g_id++) {
#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (int t_id = 0; t_id < n_b_threads; t_id++) {
      for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
           face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
           face_id++) {

        cs_real_t diipbv[3];
        cs_lnum_t ii = b_face_cells[face_id];

        for (int jsou = 0; jsou < 3; jsou++)
          diipbv[jsou] = diipb[face_id][jsou];

        /* x-y-z components, p = u, v, w */

        for (int isou = 0; isou < 6; isou++) {
          cs_real_t pfac = inc*coefa[face_id][isou];
          /*coefu is a matrix */
          for (int jsou =  0; jsou < 6; jsou++)
            pfac += coefb[face_id][jsou][isou]*(  pvar[ii][jsou]
                                                + grad[ii][jsou][0]*diipbv[0]
                                                + grad[ii][jsou][1]*diipbv[1]
                                                + grad[ii][jsou][2]*diipbv[2]);

          for (int jsou = 0; jsou < 3; jsou++)
            grdpa[ii][isou][jsou] += pfac*b_f_face_normal[face_id][jsou];
        }

      }
    }
  }

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
    cs_real_t unsvol = 1./cell_vol[cell_id];
    for (int isou = 0; isou < 6; isou++) {
      for (int jsou = 0; jsou < 3; jsou++)
        grdpa[cell_id][isou][jsou] = grdpa[cell_id][isou][jsou]*unsvol;
    }
  }

  /* Handle parallelism and periodicity */

  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)grdpa, 18);
    if (m->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(halo, halo_type, (cs_real_t *)grdpa);
  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Compute the beta blending coefficient of the
 * beta limiter (ensuring preservation of a given min/max pair of values).
 *
 * \param[in]     f_id         field id
 * \param[in]     inc          "not an increment" flag
 * \param[in]     rovsdt       rho * volume / dt
 */
/*----------------------------------------------------------------------------*/

void
cs_beta_limiter_building(int              f_id,
                         int              inc,
                         const cs_real_t  rovsdt[])
{
  const cs_mesh_t *m = cs_glob_mesh;
  const cs_halo_t *halo = m->halo;
  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;

  /* Get options from the field */

  cs_field_t *f = cs_field_by_id(f_id);
  int key_cal_opt_id = cs_field_key_id("var_cal_opt");
  cs_var_cal_opt_t var_cal_opt;

  cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);

  if (var_cal_opt.isstpc != 2)
    return;

  cs_real_t* cpro_beta = cs_field_by_id(
      cs_field_get_key_int(f, cs_field_key_id("convection_limiter_id")))->val;

  cs_real_t* denom_inf;
  cs_real_t* num_inf;
  cs_real_t* denom_sup;
  cs_real_t* num_sup;

  BFT_MALLOC(denom_inf, n_cells_ext, cs_real_t);
  BFT_MALLOC(denom_sup, n_cells_ext, cs_real_t);
  BFT_MALLOC(num_inf, n_cells_ext, cs_real_t);
  BFT_MALLOC(num_sup, n_cells_ext, cs_real_t);

  /* computation of the denominator for the inferior and superior bound */

  _beta_limiter_denom(f_id,
                      inc,
                      denom_inf,
                      denom_sup);

  /* computation of the numerator for the inferior and superior bound */

  _beta_limiter_num(f_id,
                    inc,
                    rovsdt,
                    num_inf,
                    num_sup);

# pragma omp parallel for
  for (cs_lnum_t ii = 0; ii < n_cells; ii++) {

    /* Treatment of the inferior bound */
    cs_real_t beta_inf;
    if (denom_inf[ii] <= num_inf[ii]) {
      beta_inf = 1.;
    }
    else if (denom_inf[ii] <= CS_ABS(num_inf[ii])) {
      beta_inf = -1.;
    }
    else {
      beta_inf = num_inf[ii]/denom_inf[ii]; //FIXME division by 0
      beta_inf = CS_MIN(beta_inf, 1.);
    }

    /* Treatment of the superior bound */
    cs_real_t beta_sup;
    if (denom_sup[ii] <= num_sup[ii]) {
      beta_sup = 1.;
    }
    else if (denom_sup[ii] <= CS_ABS(num_sup[ii])) {
      beta_sup = -1.;
    }
    else {
      beta_sup = num_sup[ii]/denom_sup[ii]; //FIXME division by 0
      beta_sup = CS_MIN(beta_sup, 1.);
    }

    cpro_beta[ii] = CS_MIN(beta_inf, beta_sup);
  }

  /* Synchronize variable */
  if (halo != NULL)
    cs_halo_sync_var(halo, CS_HALO_STANDARD, cpro_beta);

  BFT_FREE(denom_inf);
  BFT_FREE(num_inf);
  BFT_FREE(denom_sup);
  BFT_FREE(num_sup);
}

/*----------------------------------------------------------------------------*/
/*!
 * <a name="cs_convection_diffusion_scalar"></a>
 *
 * \brief Add the explicit part of the convection/diffusion terms of a
 * standard transport equation of a scalar field \f$ \varia \f$.
 *
 * More precisely, the right hand side \f$ Rhs \f$ is updated as
 * follows:
 * \f[
 * Rhs = Rhs - \sum_{\fij \in \Facei{\celli}}      \left(
 *        \dot{m}_\ij \left( \varia_\fij - \varia_\celli \right)
 *      - \mu_\fij \gradv_\fij \varia \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * - \f$ Rhs \f$ has already been initialized before calling bilsc2!
 * - mind the sign minus
 *
 * Please refer to the
 * <a href="../../theory.pdf#bilsc2"><b>bilsc2</b></a> section of the
 * theory guide for more informations.
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          field id (or -1)
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     icvflb        global indicator of boundary convection flux
 *                               - 0 upwind scheme at all boundary faces
 *                               - 1 imposed flux at some boundary faces
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
 *                                   (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     imasac        take mass accumulation into account?
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     icvfli        boundary face indicator array of convection flux
 *                               - 0 upwind scheme
 *                               - 1 imposed flux
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_massflux    mass flux at interior faces
 * \param[in]     b_massflux    mass flux at boundary faces
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_convection_diffusion_scalar(int                       idtvar,
                               int                       f_id,
                               const cs_var_cal_opt_t    var_cal_opt,
                               int                       icvflb,
                               int                       inc,
                               int                       iccocg,
                               int                       imasac,
                               cs_real_t       *restrict pvar,
                               const cs_real_t *restrict pvara,
                               const int                 icvfli[],
                               const cs_real_t           coefap[],
                               const cs_real_t           coefbp[],
                               const cs_real_t           cofafp[],
                               const cs_real_t           cofbfp[],
                               const cs_real_t           i_massflux[],
                               const cs_real_t           b_massflux[],
                               const cs_real_t           i_visc[],
                               const cs_real_t           b_visc[],
                               cs_real_t       *restrict rhs)
{
  const int iconvp = var_cal_opt.iconv;
  const int idiffp = var_cal_opt.idiff;
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int ischcp = var_cal_opt.ischcv;
  const int isstpp = var_cal_opt.isstpc;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  int limiter_choice = -1;
  const double blencp = var_cal_opt.blencv;
  const double blend_st = var_cal_opt.blend_st;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_face_surf = fvq->i_face_surf;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int *bc_type = cs_glob_bc_type;

  /* Local variables */

  char var_name[64];

  int iupwin = 0;
  int tr_dim = 0;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_t *coface = NULL, *cofbce = NULL;

  cs_real_3_t *grad;
  cs_real_3_t *gradup = NULL;
  cs_real_3_t *gradst = NULL;
  cs_field_t *f = NULL;

  cs_real_t *local_min = NULL;
  cs_real_t *local_max = NULL;
  cs_real_t *courant = NULL;

  cs_real_t *cv_limiter = NULL;
  cs_real_t *df_limiter = NULL;

  cs_real_t *gweight = NULL;

  const int key_lim_choice = cs_field_key_id("limiter_choice");

  cs_real_t  *v_slope_test = cs_get_v_slope_test(f_id,  var_cal_opt);

  /* Internal coupling variables */
  cs_real_t *pvar_local = NULL;
  cs_real_t *pvar_distant = NULL;
  cs_real_t *df_limiter_local = NULL;
  cs_real_t hint, hext, heq;
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  cs_lnum_t n_distant;
  cs_lnum_t *faces_distant = NULL;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /* Initialization */

  /* Allocate work arrays */

  BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL)
    cs_sync_scalar_halo(m, tr_dim, pvar);
  else if (pvara == NULL)
    pvara = (const cs_real_t *restrict)pvar;

  const cs_real_t  *restrict _pvar = (pvar != NULL) ? pvar : pvara;

  /* Limiters */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);
    cs_gradient_perio_init_rij(f, &tr_dim, grad);

    /* NVD/TVD limiters */
    if (ischcp == 4) {
      limiter_choice = cs_field_get_key_int(f, key_lim_choice);
      BFT_MALLOC(local_max, n_cells_ext, cs_real_t);
      BFT_MALLOC(local_min, n_cells_ext, cs_real_t);
      cs_field_local_extrema_scalar(f_id,
                                    halo_type,
                                    local_max,
                                    local_min);
      if (limiter_choice >= CS_NVD_VOF_HRIC) {
        BFT_MALLOC(courant, n_cells_ext, cs_real_t);
        cs_cell_courant_number(f_id, courant);
      }
    }

    int cv_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("convection_limiter_id"));
    if (cv_limiter_id > -1)
      cv_limiter = cs_field_by_id(cv_limiter_id)->val;

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else if (isstpp > 1) {
    bft_error(__FILE__, __LINE__, 0,
              _("invalid value of isstpp for a work array"));
  } else {
    strncpy(var_name, "[scalar convection-diffusion]", 63);
  }
  var_name[63] = '\0';

  if (iwarnp >= 2) {
    if (ischcp == 1) {
      bft_printf(
        _(" %s: Convection in centered blending with %f percent of upwind\n"),
        var_name, (1.-blencp)*100.);
    } else {
      bft_printf(
        _(" %s: Convection in 2nd order blending with %f percent of upwind\n"),
        var_name, (1.-blencp)*100.);
    }
  }

  iupwin = (blencp > 0.) ? 0 : 1;

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       &n_distant,
                                       &faces_distant);
  }

  /* Compute the balance with reconstruction */

  /* Compute the gradient of the variable */

  /* The gradient (grad) is used in the flux reconstruction and the slope test.
     Thus we must compute it:
         - when we have diffusion and we reconstruct the fluxes,
         - when the convection scheme is the legacy SOLU,
         - when we have convection, we are not in pure upwind
           and we reconstruct the fluxes,
         - when we have convection, we are not in pure upwind
           and we have not shunted the slope test,
         - when we use NVD / TVD schemes.
  */

  if (  (idiffp != 0 && ircflp == 1)
     || (  iconvp != 0 && iupwin == 0
        && (ischcp == 0 || ircflp == 1 || isstpp == 0 || ischcp == 3 || ischcp == 4))) {

    if (f_id != -1) {
      /* Get the calculation option from the field */
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    0, /* hyd_p_flag */
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    NULL, /* f_ext exterior force */
                                    coefap,
                                    coefbp,
                                    _pvar,
                                    gweight, /* Weighted gradient */
                                    cpl,
                                    grad);

  } else {

#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      grad[cell_id][0] = 0.;
      grad[cell_id][1] = 0.;
      grad[cell_id][2] = 0.;
    }
  }

  /* Compute gradients used in convection schemes */

  if (iconvp > 0 && iupwin == 0) {

    /* Compute cell gradient used in slope test */
    if (isstpp == 0) {

      BFT_MALLOC(gradst, n_cells_ext, cs_real_3_t);

#     pragma omp parallel for
      for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
        gradst[cell_id][0] = 0.;
        gradst[cell_id][1] = 0.;
        gradst[cell_id][2] = 0.;
      }

      cs_slope_test_gradient(f_id,
                             inc,
                             halo_type,
                             (const cs_real_3_t *)grad,
                             gradst,
                             _pvar,
                             coefap,
                             coefbp,
                             i_massflux);

    }

    /* Pure SOLU scheme */
    if (ischcp == 2) {

      BFT_MALLOC(gradup, n_cells_ext, cs_real_3_t);

#     pragma omp parallel for
      for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
        gradup[cell_id][0] = 0.;
        gradup[cell_id][1] = 0.;
        gradup[cell_id][2] = 0.;
      }

      cs_upwind_gradient(f_id,
                         inc,
                         halo_type,
                         coefap,
                         coefbp,
                         i_massflux,
                         b_massflux,
                         _pvar,
                         gradup);

    }

  }

  /* ======================================================================
    ---> Contribution from interior faces
    ======================================================================*/

  cs_gnum_t n_upwind = 0;

  if (n_cells_ext>n_cells) {
#   pragma omp parallel for if(n_cells_ext - n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      rhs[cell_id] = 0.;
    }
  }

  /* --> Pure upwind flux
    =====================*/

  if (iupwin == 1) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_upwind(bldfrp,
                                  relaxp,
                                  diipf[face_id],
                                  djjpf[face_id],
                                  grad[ii],
                                  grad[jj],
                                  _pvar[ii],
                                  _pvar[jj],
                                  pvara[ii],
                                  pvara[jj],
                                  &pifri,
                                  &pifrj,
                                  &pjfri,
                                  &pjfrj,
                                  &pip,
                                  &pjp,
                                  &pipr,
                                  &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_upwind(bldfrp,
                                    diipf[face_id],
                                    djjpf[face_id],
                                    grad[ii],
                                    grad[jj],
                                    _pvar[ii],
                                    _pvar[jj],
                                    &pif,
                                    &pjf,
                                    &pip,
                                    &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           fluxij);

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip,/* no relaxation */
                           pjp,/* no relaxation */
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    }

  /* --> Flux with no slope test or Min/Max Beta limiter
    ====================================================*/

  } else if (isstpp == 1 || isstpp == 2) {

    if (ischcp < 0 || ischcp > 4) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady(bldfrp,
                           ischcp,
                           relaxp,
                           blencp,
                           weight[face_id],
                           cell_cen[ii],
                           cell_cen[jj],
                           i_face_cog[face_id],
                           diipf[face_id],
                           djjpf[face_id],
                           grad[ii],
                           grad[jj],
                           gradup[ii],
                           gradup[jj],
                           _pvar[ii],
                           _pvar[jj],
                           pvara[ii],
                           pvara[jj],
                           &pifri,
                           &pifrj,
                           &pjfri,
                           &pjfrj,
                           &pip,
                           &pjp,
                           &pipr,
                           &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t beta = blencp;

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            /* Beta blending coefficient ensuring positivity of the scalar */
            if (isstpp == 2) {
              beta = CS_MAX(CS_MIN(cv_limiter[ii], cv_limiter[jj]), 0.);
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            if (ischcp != 4) {
              cs_real_t hybrid_coef_ii, hybrid_coef_jj;
              if (ischcp == 3) {
                hybrid_coef_ii = CS_F_(hybrid_blend)->val[ii];
                hybrid_coef_jj = CS_F_(hybrid_blend)->val[jj];
              } else {
                hybrid_coef_ii = 0.;
                hybrid_coef_jj = 0.;
              }
              cs_i_cd_unsteady(bldfrp,
                              ischcp,
                              beta,
                              weight[face_id],
                              cell_cen[ii],
                              cell_cen[jj],
                              i_face_cog[face_id],
                              hybrid_coef_ii,
                              hybrid_coef_jj,
                              diipf[face_id],
                              djjpf[face_id],
                              grad[ii],
                              grad[jj],
                              gradup[ii],
                              gradup[jj],
                              _pvar[ii],
                              _pvar[jj],
                              &pif,
                              &pjf,
                              &pip,
                              &pjp);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             1., /* xcpp */
                             1., /* xcpp */
                             fluxij);

            } else {
              /* NVD/TVD family of high accuracy schemes */

              cs_lnum_t ic, id;

              /* Determine central and downwind sides w.r.t. current face */
              cs_central_downwind_cells(ii,
                                        jj,
                                        i_massflux[face_id],
                                        &ic,  /* central cell id */
                                        &id); /* downwind cell id */

              cs_real_t courant_c = -1.;
              if (courant != NULL)
                courant_c = courant[ic];

              cs_i_cd_unsteady_nvd(limiter_choice,
                                   beta,
                                   cell_cen[ic],
                                   cell_cen[id],
                                   i_face_normal[face_id],
                                   i_face_cog[face_id],
                                   grad[ic],
                                   _pvar[ic],
                                   _pvar[id],
                                   local_max[ic],
                                   local_min[ic],
                                   courant_c,
                                   &pif,
                                   &pjf);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             1., /* xcpp */
                             1., /* xcpp */
                             fluxij);

              /* Compute required quantities for diffusive flux */
              cs_real_t recoi, recoj;

              cs_i_compute_quantities(bldfrp,
                                      diipf[face_id],
                                      djjpf[face_id],
                                      grad[ii],
                                      grad[jj],
                                      _pvar[ii],
                                      _pvar[jj],
                                      &recoi,
                                      &recoj,
                                      &pip,
                                      &pjp);
            }

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip, /* no relaxation */
                           pjp, /* no relaxation */
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    }

  /* --> Flux with slope test
    ============================================*/

  } else { /* isstpp = 0 */

    if (ischcp < 0 || ischcp > 2) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_2_t fluxij = {0., 0.};

            bool upwind_switch = false;
            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_slope_test(&upwind_switch,
                                      iconvp,
                                      bldfrp,
                                      ischcp,
                                      relaxp,
                                      blencp,
                                      blend_st,
                                      weight[face_id],
                                      i_dist[face_id],
                                      i_face_surf[face_id],
                                      cell_cen[ii],
                                      cell_cen[jj],
                                      i_face_normal[face_id],
                                      i_face_cog[face_id],
                                      diipf[face_id],
                                      djjpf[face_id],
                                      i_massflux[face_id],
                                      grad[ii],
                                      grad[jj],
                                      gradup[ii],
                                      gradup[jj],
                                      gradst[ii],
                                      gradst[jj],
                                      _pvar[ii],
                                      _pvar[jj],
                                      pvara[ii],
                                      pvara[jj],
                                      &pifri,
                                      &pifrj,
                                      &pjfri,
                                      &pjfrj,
                                      &pip,
                                      &pjp,
                                      &pipr,
                                      &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            if (upwind_switch) {

              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;
              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }

            }

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            bool upwind_switch = false;

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_slope_test(&upwind_switch,
                                        iconvp,
                                        bldfrp,
                                        ischcp,
                                        blencp,
                                        blend_st,
                                        weight[face_id],
                                        i_dist[face_id],
                                        i_face_surf[face_id],
                                        cell_cen[ii],
                                        cell_cen[jj],
                                        i_face_normal[face_id],
                                        i_face_cog[face_id],
                                        diipf[face_id],
                                        djjpf[face_id],
                                        i_massflux[face_id],
                                        grad[ii],
                                        grad[jj],
                                        gradup[ii],
                                        gradup[jj],
                                        gradst[ii],
                                        gradst[jj],
                                        _pvar[ii],
                                        _pvar[jj],
                                        &pif,
                                        &pjf,
                                        &pip,
                                        &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           fluxij);

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip, /* no relaxation */
                           pjp, /* no relaxation */
                           i_visc[face_id],
                           fluxij);

            if (upwind_switch) {
              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;

              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }
            }

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    } /* idtvar */

  } /* iupwin */


  if (iwarnp >= 2 && iconvp == 1) {

    /* Sum number of clippings */
    cs_parall_counter(&n_upwind, 1);

    bft_printf(_(" %s: %llu Faces with upwind on %llu interior faces \n"),
               var_name, (unsigned long long)n_upwind,
               (unsigned long long)m->n_g_i_c_faces);
  }

  /* ======================================================================
    ---> Contribution from boundary faces
    ======================================================================*/

  /* Boundary convective flux are all computed with an upwind scheme */
  if (icvflb == 0) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi = 0.;
            cs_real_t pir, pipr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady(bldfrp,
                           relaxp,
                           diipb[face_id],
                           grad[ii],
                           _pvar[ii],
                           pvara[ii],
                           &pir,
                           &pipr);

            cs_b_upwind_flux(iconvp,
                             1.,
                             1,
                             inc,
                             bc_type[face_id],
                             _pvar[ii],
                             pir,
                             pipr,
                             coefap[face_id],
                             coefbp[face_id],
                             b_massflux[face_id],
                             1., /* xcpp */
                             &fluxi);

            cs_b_diff_flux(idiffp,
                           1., /* thetap */
                           inc,
                           pipr,
                           cofafp[face_id],
                           cofbfp[face_id],
                           b_visc[face_id],
                           &fluxi);

            rhs[ii] -= fluxi;

          }
        }
      }

      /* The scalar is internal_coupled and an implicit contribution
       * is required */
      if (icoupl > 0) {
        /* Prepare data for sending */
        BFT_MALLOC(pvar_distant, n_distant, cs_real_t);

        for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
          cs_lnum_t face_id = faces_distant[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip, pipr;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[jj], 0.);

          cs_b_cd_steady(bldfrp,
                         relaxp,
                         diipb[face_id],
                         grad[jj],
                         _pvar[jj],
                         pvara[jj],
                         &pip,
                         &pipr);
          pvar_distant[ii] = pipr;
        }

        /* Receive data */
        BFT_MALLOC(pvar_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          pvar_distant,
                                          pvar_local);

        /* Exchange diffusion limiter */
        if (df_limiter != NULL) {
          BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
          cs_internal_coupling_exchange_var(cpl,
                                            1, /* Dimension */
                                            df_limiter,
                                            df_limiter_local);
        }

        /* Flux contribution */
        assert(f != NULL);
        cs_real_t *hintp = f->bc_coeffs->hint;
        cs_real_t *hextp = f->bc_coeffs->hext;
        for (cs_lnum_t ii = 0; ii < n_local; ii++) {
          cs_lnum_t face_id = faces_local[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip, pipr, pjpr;
          cs_real_t fluxi = 0.;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

          cs_b_cd_steady(bldfrp,
                         relaxp,
                         diipb[face_id],
                         grad[jj],
                         _pvar[jj],
                         pvara[jj],
                         &pip,
                         &pipr);

          pjpr = pvar_local[ii];

          hint = hintp[face_id];
          hext = hextp[face_id];
          heq = hint * hext / (hint + hext);

          cs_b_diff_flux_coupling(idiffp,
                                  pipr,
                                  pjpr,
                                  heq,
                                  &fluxi);

          rhs[jj] -= thetap * fluxi;
        }

        BFT_FREE(pvar_local);
        /* Sending structures are no longer needed */
        BFT_FREE(pvar_distant);
        if (df_limiter != NULL)
          BFT_FREE(df_limiter_local);
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi = 0.;
            cs_real_t pip;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady(bldfrp,
                             diipb[face_id],
                             grad[ii],
                             _pvar[ii],
                             &pip);

            cs_b_upwind_flux(iconvp,
                             thetap,
                             imasac,
                             inc,
                             bc_type[face_id],
                             _pvar[ii],
                             _pvar[ii], /* no relaxation */
                             pip,
                             coefap[face_id],
                             coefbp[face_id],
                             b_massflux[face_id],
                             1., /* xcpp */
                             &fluxi);

            cs_b_diff_flux(idiffp,
                           thetap,
                           inc,
                           pip,
                           cofafp[face_id],
                           cofbfp[face_id],
                           b_visc[face_id],
                           &fluxi);

            rhs[ii] -= fluxi;

          }
        }
      }

      /* The scalar is internally coupled and an implicit contribution
       * is required */
      if (icoupl > 0) {
        /* Prepare data for sending */
        BFT_MALLOC(pvar_distant, n_distant, cs_real_t);

        for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
          cs_lnum_t face_id = faces_distant[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[jj], 0.);

          cs_b_cd_unsteady(bldfrp,
                           diipb[face_id],
                           grad[jj],
                           _pvar[jj],
                           &pip);
          pvar_distant[ii] = pip;
        }

        /* Receive data */
        BFT_MALLOC(pvar_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          pvar_distant,
                                          pvar_local);

        /* Exchange diffusion limiter */
        if (df_limiter != NULL) {
          BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
          cs_internal_coupling_exchange_var(cpl,
                                            1, /* Dimension */
                                            df_limiter,
                                            df_limiter_local);
        }

        /* Flux contribution */
        assert(f != NULL);
        cs_real_t *hintp = f->bc_coeffs->hint;
        cs_real_t *hextp = f->bc_coeffs->hext;
        for (cs_lnum_t ii = 0; ii < n_local; ii++) {
          cs_lnum_t face_id = faces_local[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip, pjp;
          cs_real_t fluxi = 0.;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

          cs_b_cd_unsteady(bldfrp,
                           diipb[face_id],
                           grad[jj],
                           _pvar[jj],
                           &pip);

          pjp = pvar_local[ii];

          hint = hintp[face_id];
          hext = hextp[face_id];
          heq = hint * hext / (hint + hext);

          cs_b_diff_flux_coupling(idiffp,
                                  pip,
                                  pjp,
                                  heq,
                                  &fluxi);

          rhs[jj] -= thetap * fluxi;
        }

        BFT_FREE(pvar_local);
        /* Sending structures are no longer needed */
        BFT_FREE(pvar_distant);
        if (df_limiter != NULL)
          BFT_FREE(df_limiter_local);
      }
    }

  /* Boundary convective flux is imposed at some faces
     (tagged in icvfli array) */
  } else if (icvflb == 1) {

    /* Retrieve the value of the convective flux to be imposed */
    if (f_id != -1) {
      coface = f->bc_coeffs->ac;
      cofbce = f->bc_coeffs->bc;
    } else {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of icvflb and f_id"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi = 0.;
            cs_real_t pir, pipr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady(bldfrp,
                           relaxp,
                           diipb[face_id],
                           grad[ii],
                           _pvar[ii],
                           pvara[ii],
                           &pir,
                           &pipr);

            cs_b_imposed_conv_flux(iconvp,
                                   1.,
                                   1,
                                   inc,
                                   bc_type[face_id],
                                   icvfli[face_id],
                                   _pvar[ii],
                                   pir,
                                   pipr,
                                   coefap[face_id],
                                   coefbp[face_id],
                                   coface[face_id],
                                   cofbce[face_id],
                                   b_massflux[face_id],
                                   1., /* xcpp */
                                   &fluxi);

            cs_b_diff_flux(idiffp,
                           1., /* thetap */
                           inc,
                           pipr,
                           cofafp[face_id],
                           cofbfp[face_id],
                           b_visc[face_id],
                           &fluxi);

            rhs[ii] -= fluxi;

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi = 0.;
            cs_real_t pip;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady(bldfrp,
                             diipb[face_id],
                             grad[ii],
                             _pvar[ii],
                             &pip);

            cs_b_imposed_conv_flux(iconvp,
                                   thetap,
                                   imasac,
                                   inc,
                                   bc_type[face_id],
                                   icvfli[face_id],
                                   _pvar[ii],
                                   _pvar[ii], /* no relaxation */
                                   pip,
                                   coefap[face_id],
                                   coefbp[face_id],
                                   coface[face_id],
                                   cofbce[face_id],
                                   b_massflux[face_id],
                                   1., /* xcpp */
                                   &fluxi);

            cs_b_diff_flux(idiffp,
                           thetap,
                           inc,
                           pip,
                           cofafp[face_id],
                           cofbfp[face_id],
                           b_visc[face_id],
                           &fluxi);

            rhs[ii] -= fluxi;

          }
        }
      }

    }
  }

  /* Free memory */
  BFT_FREE(grad);
  BFT_FREE(gradup);
  BFT_FREE(gradst);
  BFT_FREE(local_max);
  BFT_FREE(local_min);
  BFT_FREE(courant);
}

/*----------------------------------------------------------------------------*/
/*!
 * <a name="cs_face_convection_scalar"></a>
 *
 * \brief Update face flux with convection contribution of a standard transport
 * equation of a scalar field \f$ \varia \f$.
 *
 * \f[
 * C_\ij = \dot{m}_\ij \left( \varia_\fij - \varia_\celli \right)
 * \f]
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          field id (or -1)
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     icvflb        global indicator of boundary convection flux
 *                               - 0 upwind scheme at all boundary faces
 *                               - 1 imposed flux at some boundary faces
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
 *                                   (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     imasac        take mass accumulation into account?
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     icvfli        boundary face indicator array of convection flux
 *                               - 0 upwind scheme
 *                               - 1 imposed flux
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     i_massflux    mass flux at interior faces
 * \param[in]     b_massflux    mass flux at boundary faces
 * \param[in,out] i_conv_flux   scalar convection flux at interior faces
 * \param[in,out] b_conv_flux   scalar convection flux at boundary faces
 */
/*----------------------------------------------------------------------------*/

void
cs_face_convection_scalar(int                       idtvar,
                          int                       f_id,
                          const cs_var_cal_opt_t    var_cal_opt,
                          int                       icvflb,
                          int                       inc,
                          int                       iccocg,
                          int                       imasac,
                          cs_real_t       *restrict pvar,
                          const cs_real_t *restrict pvara,
                          const int                 icvfli[],
                          const cs_real_t           coefap[],
                          const cs_real_t           coefbp[],
                          const cs_real_t           i_massflux[],
                          const cs_real_t           b_massflux[],
                          cs_real_2_t               i_conv_flux[],
                          cs_real_t                 b_conv_flux[])
{
  const int iconvp = var_cal_opt.iconv;
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int ischcp = var_cal_opt.ischcv;
  const int isstpp = var_cal_opt.isstpc;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  int limiter_choice = -1;
  const double blencp = var_cal_opt.blencv;
  const double blend_st = var_cal_opt.blend_st;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_face_surf = fvq->i_face_surf;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int *bc_type = cs_glob_bc_type;

  /* Local variables */

  char var_name[64];

  int iupwin = 0;
  int tr_dim = 0;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_t *coface = NULL, *cofbce = NULL;

  cs_real_3_t *grad;
  cs_real_3_t *gradup = NULL;
  cs_real_3_t *gradst = NULL;
  cs_field_t *f = NULL;

  cs_real_t *local_min = NULL;
  cs_real_t *local_max = NULL;
  cs_real_t *courant = NULL;

  cs_real_t *cv_limiter = NULL;
  cs_real_t *df_limiter = NULL;

  cs_real_t *gweight = NULL;

  const int key_lim_choice = cs_field_key_id("limiter_choice");

  cs_real_t  *v_slope_test = cs_get_v_slope_test(f_id,  var_cal_opt);

  /* Internal coupling variables */
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /* Initialization */

  /* Allocate work arrays */

  BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL)
    cs_sync_scalar_halo(m, tr_dim, pvar);
  else if (pvara == NULL)
    pvara = (const cs_real_t *restrict)pvar;

  const cs_real_t  *restrict _pvar = (pvar != NULL) ? pvar : pvara;

  /* Slope limiters */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);
    cs_gradient_perio_init_rij(f, &tr_dim, grad);

    /* NVD/TVD limiters */
    if (ischcp == 4) {
      limiter_choice = cs_field_get_key_int(f, key_lim_choice);
      BFT_MALLOC(local_max, n_cells_ext, cs_real_t);
      BFT_MALLOC(local_min, n_cells_ext, cs_real_t);
      cs_field_local_extrema_scalar(f_id,
                                    halo_type,
                                    local_max,
                                    local_min);
      if (limiter_choice >= CS_NVD_VOF_HRIC) {
        BFT_MALLOC(courant, n_cells_ext, cs_real_t);
        cs_cell_courant_number(f_id, courant);
      }
    }

    int cv_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("convection_limiter_id"));
    if (cv_limiter_id > -1)
      cv_limiter = cs_field_by_id(cv_limiter_id)->val;

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else if (isstpp > 1) {
    bft_error(__FILE__, __LINE__, 0,
              _("invalid value of isstpp for a work array"));
  } else {
    strncpy(var_name, "[scalar face flux from convection]", 63);
  }
  var_name[63] = '\0';

  if (iwarnp >= 2) {
    if (ischcp == 1) {
      bft_printf(
        _(" %s: Convection in centered blending with %f percent of upwind\n"),
        var_name, (1.-blencp)*100.);
    } else {
      bft_printf(
        _(" %s: Convection in 2nd order blending with %f percent of upwind\n"),
        var_name, (1.-blencp)*100.);
    }
  }

  iupwin = (blencp > 0.) ? 0 : 1;

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
  }

  /* Compute the balance with reconstruction */

  /* Compute the gradient of the variable */

  /* The gradient (grad) is used in the flux reconstruction and the slope test.
     Thus we must compute it:
         - when the convection scheme is the legacy SOLU,
         - when we have convection, we are not in pure upwind
           and we reconstruct the fluxes,
         - when we have convection, we are not in pure upwind
           and we have not shunted the slope test,
         - when we use NVD / TVD schemes.
  */

  if (   iconvp != 0 && iupwin == 0
      && (ischcp == 0 || ircflp == 1 || isstpp == 0 || ischcp == 4)) {

    if (f_id != -1) {
      /* Get the calculation option from the field */
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    0, /* hyd_p_flag */
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    NULL, /* f_ext exterior force */
                                    coefap,
                                    coefbp,
                                    _pvar,
                                    gweight, /* Weighted gradient */
                                    cpl,
                                    grad);

  } else {

#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      grad[cell_id][0] = 0.;
      grad[cell_id][1] = 0.;
      grad[cell_id][2] = 0.;
    }
  }

  /* Compute gradients used in convection schemes */

  if (iconvp > 0 && iupwin == 0) {

    /* Compute cell gradient used in slope test */
    if (isstpp == 0) {

      BFT_MALLOC(gradst, n_cells_ext, cs_real_3_t);

#     pragma omp parallel for
      for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
        gradst[cell_id][0] = 0.;
        gradst[cell_id][1] = 0.;
        gradst[cell_id][2] = 0.;
      }

      cs_slope_test_gradient(f_id,
                             inc,
                             halo_type,
                             (const cs_real_3_t *)grad,
                             gradst,
                             _pvar,
                             coefap,
                             coefbp,
                             i_massflux);

    }

    /* Pure SOLU scheme */
    if (ischcp == 2) {

      BFT_MALLOC(gradup, n_cells_ext, cs_real_3_t);

#     pragma omp parallel for
      for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
        gradup[cell_id][0] = 0.;
        gradup[cell_id][1] = 0.;
        gradup[cell_id][2] = 0.;
      }

      cs_upwind_gradient(f_id,
                         inc,
                         halo_type,
                         coefap,
                         coefbp,
                         i_massflux,
                         b_massflux,
                         _pvar,
                         gradup);

    }

  }

  /* ======================================================================
    ---> Contribution from interior faces
    ======================================================================*/

  cs_gnum_t n_upwind = 0;

  /* --> Pure upwind flux
    =====================*/

  if (iupwin == 1) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_upwind(bldfrp,
                                  relaxp,
                                  diipf[face_id],
                                  djjpf[face_id],
                                  grad[ii],
                                  grad[jj],
                                  _pvar[ii],
                                  _pvar[jj],
                                  pvara[ii],
                                  pvara[jj],
                                  &pifri,
                                  &pifrj,
                                  &pjfri,
                                  &pjfrj,
                                  &pip,
                                  &pjp,
                                  &pipr,
                                  &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           i_conv_flux[face_id]);

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_upwind(bldfrp,
                                    diipf[face_id],
                                    djjpf[face_id],
                                    grad[ii],
                                    grad[jj],
                                    _pvar[ii],
                                    _pvar[jj],
                                    &pif,
                                    &pjf,
                                    &pip,
                                    &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           i_conv_flux[face_id]);

          }
        }
      }

    }

  /* --> Flux with no slope test or Min/Max Beta limiter
    ====================================================*/

  } else if (isstpp == 1 || isstpp == 2) {

    if (ischcp < 0 || ischcp > 4) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady(bldfrp,
                           ischcp,
                           relaxp,
                           blencp,
                           weight[face_id],
                           cell_cen[ii],
                           cell_cen[jj],
                           i_face_cog[face_id],
                           diipf[face_id],
                           djjpf[face_id],
                           grad[ii],
                           grad[jj],
                           gradup[ii],
                           gradup[jj],
                           _pvar[ii],
                           _pvar[jj],
                           pvara[ii],
                           pvara[jj],
                           &pifri,
                           &pifrj,
                           &pjfri,
                           &pjfrj,
                           &pip,
                           &pjp,
                           &pipr,
                           &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           i_conv_flux[face_id]);

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t beta = blencp;

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            /* Beta blending coefficient ensuring positivity of the scalar */
            if (isstpp == 2) {
              beta = CS_MAX(CS_MIN(cv_limiter[ii], cv_limiter[jj]), 0.);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            if (ischcp != 4) {
              cs_real_t hybrid_coef_ii, hybrid_coef_jj;
              if (ischcp == 3) {
                hybrid_coef_ii = CS_F_(hybrid_blend)->val[ii];
                hybrid_coef_jj = CS_F_(hybrid_blend)->val[jj];
              } else {
                hybrid_coef_ii = 0.;
                hybrid_coef_jj = 0.;
              }
              cs_i_cd_unsteady(bldfrp,
                               ischcp,
                               beta,
                               weight[face_id],
                               cell_cen[ii],
                               cell_cen[jj],
                               i_face_cog[face_id],
                               hybrid_coef_ii,
                               hybrid_coef_jj,
                               diipf[face_id],
                               djjpf[face_id],
                               grad[ii],
                               grad[jj],
                               gradup[ii],
                               gradup[jj],
                               _pvar[ii],
                               _pvar[jj],
                               &pif,
                               &pjf,
                               &pip,
                               &pjp);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             1., /* xcpp */
                             1., /* xcpp */
                             i_conv_flux[face_id]);
            } else {
              /* NVD/TVD family of high accuracy schemes */

              cs_lnum_t ic, id;

              /* Determine central and downwind sides w.r.t. current face */
              cs_central_downwind_cells(ii,
                                        jj,
                                        i_massflux[face_id],
                                        &ic,  /* central cell id */
                                        &id); /* downwind cell id */

              cs_real_t courant_c = -1.;
              if (courant != NULL)
                courant_c = courant[ic];

              cs_i_cd_unsteady_nvd(limiter_choice,
                                   beta,
                                   cell_cen[ic],
                                   cell_cen[id],
                                   i_face_normal[face_id],
                                   i_face_cog[face_id],
                                   grad[ic],
                                   _pvar[ic],
                                   _pvar[id],
                                   local_max[ic],
                                   local_min[ic],
                                   courant_c,
                                   &pif,
                                   &pjf);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             1., /* xcpp */
                             1., /* xcpp */
                             i_conv_flux[face_id]);
            }

          }
        }
      }

    }

  /* --> Flux with slope test or NVD/TVD limiter
    ============================================*/

  } else { /* isstpp = 0 */

    if (ischcp < 0 || ischcp > 2) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            bool upwind_switch = false;
            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_slope_test(&upwind_switch,
                                      iconvp,
                                      bldfrp,
                                      ischcp,
                                      relaxp,
                                      blencp,
                                      blend_st,
                                      weight[face_id],
                                      i_dist[face_id],
                                      i_face_surf[face_id],
                                      cell_cen[ii],
                                      cell_cen[jj],
                                      i_face_normal[face_id],
                                      i_face_cog[face_id],
                                      diipf[face_id],
                                      djjpf[face_id],
                                      i_massflux[face_id],
                                      grad[ii],
                                      grad[jj],
                                      gradup[ii],
                                      gradup[jj],
                                      gradst[ii],
                                      gradst[jj],
                                      _pvar[ii],
                                      _pvar[jj],
                                      pvara[ii],
                                      pvara[jj],
                                      &pifri,
                                      &pifrj,
                                      &pjfri,
                                      &pjfrj,
                                      &pip,
                                      &pjp,
                                      &pipr,
                                      &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           i_conv_flux[face_id]);

            if (upwind_switch) {

              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;
              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }

            }

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            bool upwind_switch = false;

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_slope_test(&upwind_switch,
                                        iconvp,
                                        bldfrp,
                                        ischcp,
                                        blencp,
                                        blend_st,
                                        weight[face_id],
                                        i_dist[face_id],
                                        i_face_surf[face_id],
                                        cell_cen[ii],
                                        cell_cen[jj],
                                        i_face_normal[face_id],
                                        i_face_cog[face_id],
                                        diipf[face_id],
                                        djjpf[face_id],
                                        i_massflux[face_id],
                                        grad[ii],
                                        grad[jj],
                                        gradup[ii],
                                        gradup[jj],
                                        gradst[ii],
                                        gradst[jj],
                                        _pvar[ii],
                                        _pvar[jj],
                                        &pif,
                                        &pjf,
                                        &pip,
                                        &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           1., /* xcpp */
                           1., /* xcpp */
                           i_conv_flux[face_id]);

            if (upwind_switch) {
              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;

              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }
            }

          }
        }
      }

    } /* idtvar */

  } /* iupwin */


  if (iwarnp >= 2 && iconvp == 1) {

    /* Sum number of clippings */
    cs_parall_counter(&n_upwind, 1);

    bft_printf(_(" %s: %llu Faces with upwind on %llu interior faces \n"),
               var_name, (unsigned long long)n_upwind,
               (unsigned long long)m->n_g_i_c_faces);
  }

  /* ======================================================================
    ---> Contribution from boundary faces
    ======================================================================*/

  /* Boundary convective flux are all computed with an upwind scheme */
  if (icvflb == 0) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t pir, pipr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady(bldfrp,
                           relaxp,
                           diipb[face_id],
                           grad[ii],
                           _pvar[ii],
                           pvara[ii],
                           &pir,
                           &pipr);

            cs_b_upwind_flux(iconvp,
                             1.,
                             1,
                             inc,
                             bc_type[face_id],
                             _pvar[ii],
                             pir,
                             pipr,
                             coefap[face_id],
                             coefbp[face_id],
                             b_massflux[face_id],
                             1., /* xcpp */
                             &(b_conv_flux[face_id]));

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t pip;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady(bldfrp,
                             diipb[face_id],
                             grad[ii],
                             _pvar[ii],
                             &pip);

            cs_b_upwind_flux(iconvp,
                             thetap,
                             imasac,
                             inc,
                             bc_type[face_id],
                             _pvar[ii],
                             _pvar[ii], /* no relaxation */
                             pip,
                             coefap[face_id],
                             coefbp[face_id],
                             b_massflux[face_id],
                             1., /* xcpp */
                             &(b_conv_flux[face_id]));

          }
        }
      }
    }

  /* Boundary convective flux is imposed at some faces
     (tagged in icvfli array) */
  } else if (icvflb == 1) {

    /* Retrieve the value of the convective flux to be imposed */
    if (f_id != -1) {
      coface = f->bc_coeffs->ac;
      cofbce = f->bc_coeffs->bc;
    } else {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of icvflb and f_id"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t pir, pipr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady(bldfrp,
                           relaxp,
                           diipb[face_id],
                           grad[ii],
                           _pvar[ii],
                           pvara[ii],
                           &pir,
                           &pipr);

            cs_b_imposed_conv_flux(iconvp,
                                   1.,
                                   1,
                                   inc,
                                   bc_type[face_id],
                                   icvfli[face_id],
                                   _pvar[ii],
                                   pir,
                                   pipr,
                                   coefap[face_id],
                                   coefbp[face_id],
                                   coface[face_id],
                                   cofbce[face_id],
                                   b_massflux[face_id],
                                   1., /* xcpp */
                                   &(b_conv_flux[face_id]));

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t pip;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady(bldfrp,
                             diipb[face_id],
                             grad[ii],
                             _pvar[ii],
                             &pip);

            cs_b_imposed_conv_flux(iconvp,
                                   thetap,
                                   imasac,
                                   inc,
                                   bc_type[face_id],
                                   icvfli[face_id],
                                   _pvar[ii],
                                   _pvar[ii], /* no relaxation */
                                   pip,
                                   coefap[face_id],
                                   coefbp[face_id],
                                   coface[face_id],
                                   cofbce[face_id],
                                   b_massflux[face_id],
                                   1., /* xcpp */
                                   &(b_conv_flux[face_id]));

          }
        }
      }

    }
  }

  /* Free memory */
  BFT_FREE(grad);
  BFT_FREE(gradup);
  BFT_FREE(gradst);
  BFT_FREE(local_max);
  BFT_FREE(local_min);
  BFT_FREE(courant);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the convection/diffusion terms of a transport
 *  equation of a vector field \f$ \vect{\varia} \f$.
 *
 * More precisely, the right hand side \f$ \vect{Rhs} \f$ is updated as
 * follows:
 * \f[
 *  \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}}      \left(
 *         \dot{m}_\ij \left( \vect{\varia}_\fij - \vect{\varia}_\celli \right)
 *       - \mu_\fij \gradt_\fij \vect{\varia} \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Remark:
 * if ivisep = 1, then we also take \f$ \mu \transpose{\gradt\vect{\varia}}
 * + \lambda \trace{\gradt\vect{\varia}} \f$, where \f$ \lambda \f$ is
 * the secondary viscosity, i.e. usually \f$ -\frac{2}{3} \mu \f$.
 *
 * Warning:
 * - \f$ \vect{Rhs} \f$ has already been initialized before calling bilsc!
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     icvflb        global indicator of boundary convection flux
 *                               - 0 upwind scheme at all boundary faces
 *                               - 1 imposed flux at some boundary faces
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     ivisep        indicator to take \f$ \divv
 *                               \left(\mu \gradt \transpose{\vect{a}} \right)
 *                               -2/3 \grad\left( \mu \dive \vect{a} \right)\f$
 *                               - 1 take into account,
 *                               - 0 otherwise
 * \param[in]     imasac        take mass accumulation into account?
 * \param[in]     pvar          solved velocity (current time step)
 * \param[in]     pvara         solved velocity (previous time step)
 * \param[in]     icvfli        boundary face indicator array of convection flux
 *                               - 0 upwind scheme
 *                               - 1 imposed flux
 * \param[in]     coefav        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbv        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafv        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfv        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_massflux    mass flux at interior faces
 * \param[in]     b_massflux    mass flux at boundary faces
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     i_secvis      secondary viscosity at interior faces
 * \param[in]     b_secvis      secondary viscosity at boundary faces
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_convection_diffusion_vector(int                         idtvar,
                               int                         f_id,
                               const cs_var_cal_opt_t      var_cal_opt,
                               int                         icvflb,
                               int                         inc,
                               int                         ivisep,
                               int                         imasac,
                               cs_real_3_t       *restrict pvar,
                               const cs_real_3_t *restrict pvara,
                               const int                   icvfli[],
                               const cs_real_3_t           coefav[],
                               const cs_real_33_t          coefbv[],
                               const cs_real_3_t           cofafv[],
                               const cs_real_33_t          cofbfv[],
                               const cs_real_t             i_massflux[],
                               const cs_real_t             b_massflux[],
                               const cs_real_t             i_visc[],
                               const cs_real_t             b_visc[],
                               const cs_real_t             i_secvis[],
                               const cs_real_t             b_secvis[],
                               cs_real_3_t       *restrict rhs)
{
  const int iconvp = var_cal_opt.iconv;
  const int idiffp = var_cal_opt.idiff;
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int ischcp = var_cal_opt.ischcv;
  const int isstpp = var_cal_opt.isstpc;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  const double blencp = var_cal_opt.blencv;
  const double blend_st = var_cal_opt.blend_st;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_face_surf = fvq->i_face_surf;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_f_face_normal
    = (const cs_real_3_t *restrict)fvq->i_f_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict b_f_face_normal
    = (const cs_real_3_t *restrict)fvq->b_f_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int *bc_type = cs_glob_bc_type;
  cs_real_2_t *i_f_face_factor = NULL;
  cs_real_t *b_f_face_factor = NULL;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  cs_field_t *f = NULL;
  char var_name[64];

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[convection-diffusion, vector]", 63);
  var_name[63] = '\0';

  /* Discontinuous porous treatment */
  if (cs_glob_porous_model == 3 && f == CS_F_(vel)) {
    i_f_face_factor = fvq->i_f_face_factor;
    b_f_face_factor = fvq->b_f_face_factor;
  }

  cs_gnum_t n_upwind;
  int iupwin = 0;

  cs_real_33_t *grad, *grdpa;
  cs_real_t *bndcel;

  const cs_real_3_t *coface = NULL;
  const cs_real_33_t *cofbce = NULL;

  cs_real_t *gweight = NULL;

  cs_real_t  *v_slope_test = cs_get_v_slope_test(f_id,  var_cal_opt);

  /* Internal coupling variables */
  cs_real_3_t *pvar_local = NULL;
  cs_real_3_t *pvar_distant = NULL;
  cs_real_t *df_limiter_local = NULL;
  cs_real_t hint, hext, heq;
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  cs_lnum_t n_distant;
  cs_lnum_t *faces_distant = NULL;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /*==========================================================================*/

  /* 1. Initialization */

  /* Allocate work arrays */

  BFT_MALLOC(grad, n_cells_ext, cs_real_33_t);
  BFT_MALLOC(grdpa, n_cells_ext, cs_real_33_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL && halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)pvar, 3);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_vect(halo, halo_type, (cs_real_t *)pvar, 3);
  }
  else if (pvara == NULL)
    pvara = (const cs_real_3_t *restrict)pvar;

  const cs_real_3_t  *restrict _pvar
    = (pvar != NULL) ? (const cs_real_3_t  *restrict)pvar : pvara;

  /* Slope limiters */

  if (iwarnp >= 2 && iconvp == 1) {
    if (ischcp == 1) {
      bft_printf
        (
         _(" %s: Convection in centered blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    } else {
      bft_printf
        (
         _(" %s: Convection in 2nd order blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    }
  }

  iupwin = (blencp > 0.) ? 0 : 1;

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       &n_distant,
                                       &faces_distant);
  }

  /* 2. Compute the balance with reconstruction */

  /* Compute the gradient of the velocity

     The gradient (grad) is used in the flux reconstruction and the slope test.
     Thus we must compute it:
         - when we have diffusion and we reconstruct the fluxes,
         - when the convection scheme is SOLU,
         - when we have convection, we are not in pure upwind
           and we reconstruct the fluxes,
         - when we have convection, we are not in pure upwind
           and we have not shunted the slope test. */

  if (  (idiffp != 0 && ircflp == 1) || ivisep == 1
     || (   iconvp != 0 && iupwin == 0
         && (ischcp == 0 || ircflp == 1 || isstpp == 0))) {

    if (f_id != -1) {
      /* Get the calculation option from the field */
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_vector_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    nswrgp,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    coefav,
                                    coefbv,
                                    _pvar,
                                    gweight, /* weighted gradient */
                                    cpl,
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++) {
        for (int jsou = 0; jsou < 3; jsou++)
          grad[cell_id][isou][jsou] = 0.;
      }
    }
  }

  /* ======================================================================
     ---> Compute uncentered gradient grdpa for the slope test
     ======================================================================*/

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
    for (int jsou = 0; jsou < 3; jsou++) {
      for (int isou = 0; isou < 3; isou++)
        grdpa[cell_id][isou][jsou] = 0.;
    }
  }

  if (iconvp > 0 && iupwin == 0 && isstpp == 0) {

    cs_slope_test_gradient_vector(inc,
                                  halo_type,
                                  (const cs_real_33_t *)grad,
                                  grdpa,
                                  _pvar,
                                  coefav,
                                  coefbv,
                                  i_massflux);

  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  n_upwind = 0;

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext -n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++)
        rhs[cell_id][isou] = 0.;
    }
  }

  /* --> Pure upwind flux
     =====================*/

  if (iupwin == 1) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_t fluxi[3], fluxj[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }

            cs_real_3_t pip, pjp, pipr, pjpr;
            cs_real_3_t pifri, pifrj, pjfri, pjfrj;
            cs_real_3_t _pi, _pj, _pia, _pja;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
              _pia[i] = pvara[ii][i];
              _pja[i] = pvara[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pia);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pja);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_upwind_vector(bldfrp,
                                         relaxp,
                                         diipf[face_id],
                                         djjpf[face_id],
                                         (const cs_real_3_t *)grad[ii],
                                         (const cs_real_3_t *)grad[jj],
                                         _pi,
                                         _pj,
                                         _pia,
                                         _pja,
                                         pifri,
                                         pifrj,
                                         pjfri,
                                         pjfrj,
                                         pip,
                                         pjp,
                                         pipr,
                                         pjpr);


            cs_i_conv_flux_vector(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

           for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_t fluxi[3], fluxj[3] ;
            for (int i = 0; i < 3; i++) {
              fluxi[i] = 0;
              fluxj[i] = 0;
            }
            cs_real_3_t pip, pjp;
            cs_real_3_t pif, pjf;
            cs_real_3_t _pi, _pj;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_upwind_vector(bldfrp,
                                           diipf[face_id],
                                           djjpf[face_id],
                                           (const cs_real_3_t *)grad[ii],
                                           (const cs_real_3_t *)grad[jj],
                                           _pi,
                                           _pj,
                                           pif,
                                           pjf,
                                           pip,
                                           pjp);

            cs_i_conv_flux_vector(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

    }

    /* --> Flux with no slope test
       ============================*/

  } else if (isstpp == 1) {

    if (ischcp < 0 || ischcp == 2 || ischcp > 3) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t fluxi[3], fluxj[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_3_t pip, pjp, pipr, pjpr;
            cs_real_3_t pifri, pifrj, pjfri, pjfrj;
            cs_real_3_t _pi, _pj, _pia, _pja;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
              _pia[i] = pvara[ii][i];
              _pja[i] = pvara[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pia);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pja);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_vector(bldfrp,
                                  ischcp,
                                  relaxp,
                                  blencp,
                                  weight[face_id],
                                  cell_cen[ii],
                                  cell_cen[jj],
                                  i_face_cog[face_id],
                                  diipf[face_id],
                                  djjpf[face_id],
                                  (const cs_real_3_t *)grad[ii],
                                  (const cs_real_3_t *)grad[jj],
                                  _pi,
                                  _pj,
                                  _pia,
                                  _pja,
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr);

            cs_i_conv_flux_vector(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t fluxi[3], fluxj[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }

            cs_real_3_t pip, pjp;
            cs_real_3_t pif, pjf;
            cs_real_3_t _pi, _pj;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
            }

            cs_real_t hybrid_coef_ii, hybrid_coef_jj;
            if (ischcp == 3) {
              hybrid_coef_ii = CS_F_(hybrid_blend)->val[ii];
              hybrid_coef_jj = CS_F_(hybrid_blend)->val[jj];
            } else {
              hybrid_coef_ii = 0.;
              hybrid_coef_jj = 0.;
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_vector(bldfrp,
                                    ischcp,
                                    blencp,
                                    weight[face_id],
                                    cell_cen[ii],
                                    cell_cen[jj],
                                    i_face_cog[face_id],
                                    hybrid_coef_ii,
                                    hybrid_coef_jj,
                                    diipf[face_id],
                                    djjpf[face_id],
                                    (const cs_real_3_t *)grad[ii],
                                    (const cs_real_3_t *)grad[jj],
                                    _pi,
                                    _pj,
                                    pif,
                                    pjf,
                                    pip,
                                    pjp);

            cs_i_conv_flux_vector(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

    }

    /* --> Flux with slope test
       =========================*/

  } else {

    if (ischcp < 0 || ischcp > 1) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t fluxi[3], fluxj[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_3_t pip, pjp, pipr, pjpr;
            cs_real_3_t pifri, pifrj, pjfri, pjfrj;
            bool upwind_switch = false;
            cs_real_3_t _pi, _pj, _pia, _pja;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
              _pia[i] = pvara[ii][i];
              _pja[i] = pvara[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pia);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pja);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_slope_test_vector(&upwind_switch,
                                             iconvp,
                                             bldfrp,
                                             ischcp,
                                             relaxp,
                                             blencp,
                                             blend_st,
                                             weight[face_id],
                                             i_dist[face_id],
                                             i_face_surf[face_id],
                                             cell_cen[ii],
                                             cell_cen[jj],
                                             i_face_normal[face_id],
                                             i_face_cog[face_id],
                                             diipf[face_id],
                                             djjpf[face_id],
                                             i_massflux[face_id],
                                             (const cs_real_3_t *)grad[ii],
                                             (const cs_real_3_t *)grad[jj],
                                             (const cs_real_3_t *)grdpa[ii],
                                             (const cs_real_3_t *)grdpa[jj],
                                             _pi,
                                             _pj,
                                             _pia,
                                             _pja,
                                             pifri,
                                             pifrj,
                                             pjfri,
                                             pjfrj,
                                             pip,
                                             pjp,
                                             pipr,
                                             pjpr);

            cs_i_conv_flux_vector(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t fluxi[3], fluxj[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_3_t pip, pjp;
            cs_real_3_t pif, pjf;
            bool upwind_switch = false;
            cs_real_3_t _pi, _pj;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pj[i]  = _pvar[jj][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (i_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(i_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][0], _pi);
              cs_math_3_normal_scaling(n, i_f_face_factor[face_id][1], _pj);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_slope_test_vector(&upwind_switch,
                                               iconvp,
                                               bldfrp,
                                               ischcp,
                                               blencp,
                                               blend_st,
                                               weight[face_id],
                                               i_dist[face_id],
                                               i_face_surf[face_id],
                                               cell_cen[ii],
                                               cell_cen[jj],
                                               i_face_normal[face_id],
                                               i_face_cog[face_id],
                                               diipf[face_id],
                                               djjpf[face_id],
                                               i_massflux[face_id],
                                               (const cs_real_3_t *)grad[ii],
                                               (const cs_real_3_t *)grad[jj],
                                               (const cs_real_3_t *)grdpa[ii],
                                               (const cs_real_3_t *)grdpa[jj],
                                               _pi,
                                               _pj,
                                               pif,
                                               pjf,
                                               pip,
                                               pjp);

            cs_i_conv_flux_vector(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_vector(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            if (upwind_switch) {

              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;

              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }
            }

            for (int isou = 0; isou < 3; isou++) {

              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];

            } /* isou */

          }
        }
      }

    } /* idtvar */

  } /* iupwin */

  if (iwarnp >= 2 && iconvp == 1) {

    /* Sum number of clippings */
    cs_parall_counter(&n_upwind, 1);

    bft_printf(_(" %s: %llu Faces with upwind on %llu interior faces \n"),
               var_name, (unsigned long long)n_upwind,
               (unsigned long long)m->n_g_i_c_faces);
  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Boundary convective flux are all computed with an upwind scheme */
  if (icvflb == 0) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_3_t pir, pipr;
            cs_real_3_t _pi, _pia;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pia[i] = pvara[ii][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (b_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(b_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pi);
              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pia);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady_vector(bldfrp,
                                  relaxp,
                                  diipb[face_id],
                                  (const cs_real_3_t *)grad[ii],
                                  _pi,
                                  _pia,
                                  pir,
                                  pipr);

            cs_b_upwind_flux_vector(iconvp,
                                    1., /* thetap */
                                    1, /* imasac */
                                    inc,
                                    bc_type[face_id],
                                    _pi,
                                    pir,
                                    pipr,
                                    coefav[face_id],
                                    coefbv[face_id],
                                    b_massflux[face_id],
                                    fluxi);

            cs_b_diff_flux_vector(idiffp,
                                  1., /* thetap */
                                  inc,
                                  pipr,
                                  cofafv[face_id],
                                  cofbfv[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            } /* isou */

          }
        }
      }

      if (icoupl > 0) {
        /* Prepare data for sending */
        BFT_MALLOC(pvar_distant, n_distant, cs_real_3_t);

        for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
          cs_lnum_t face_id = faces_distant[ii];
          cs_lnum_t jj = b_face_cells[face_id];

          cs_real_3_t pip, pipr;
          cs_real_3_t _pj, _pja;

          for (int i = 0; i < 3; i++) {
            _pj[i]  = _pvar[jj][i];
            _pja[i]  = pvara[jj][i];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          /* Note: to be treated exactly as a internal face, should be a bending
           * between the two cells... */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[jj], 0.);

          /* Scaling due to mass balance in porous modelling */
          if (b_f_face_factor != NULL) {
            cs_real_3_t n;
            cs_math_3_normalise(b_face_normal[face_id], n);

            cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pj);
          }

          cs_b_cd_steady_vector(bldfrp,
                                relaxp,
                                diipb[face_id],
                                (const cs_real_3_t *)grad[jj],
                                _pj,
                                _pja,
                                pip,
                                pipr);

          for (int k = 0; k < 3; k++)
            pvar_distant[ii][k] = pipr[k];
        }

        /* Receive data */
        BFT_MALLOC(pvar_local, n_local, cs_real_3_t);
        cs_internal_coupling_exchange_var(cpl,
                                          3, /* Dimension */
                                          (cs_real_t *)pvar_distant,
                                          (cs_real_t *)pvar_local);

        if (df_limiter != NULL) {
          BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
          cs_internal_coupling_exchange_var(cpl,
                                            1, /* Dimension */
                                            df_limiter,
                                            df_limiter_local);
        }

        /* Flux contribution */
        assert(f != NULL);
        cs_real_t *hintp = f->bc_coeffs->hint;
        cs_real_t *hextp = f->bc_coeffs->hext;
        for (cs_lnum_t ii = 0; ii < n_local; ii++) {
          cs_lnum_t face_id = faces_local[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip[3], pipr[3], pjpr[3];
          cs_real_t fluxi[3] = {0., 0., 0.};
          cs_real_3_t _pj, _pja;

          for (cs_lnum_t i = 0; i < 3; i++) {
            _pj[i]  = _pvar[jj][i];
            _pja[i]  = pvara[jj][i];
          }

          /* Scaling due to mass balance in porous modelling */
          if (b_f_face_factor != NULL) {
            cs_real_3_t n;
            cs_math_3_normalise(b_face_normal[face_id], n);

            cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pj);
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

          cs_b_cd_steady_vector(bldfrp,
                                relaxp,
                                diipb[face_id],
                                (const cs_real_3_t *)grad[jj],
                                _pj,
                                _pja,
                                pip,
                                pipr);

          for (cs_lnum_t k = 0; k < 3; k++)
            pjpr[k] = pvar_local[ii][k];

          hint = hintp[face_id];
          hext = hextp[face_id];
          heq = hint * hext / (hint + hext);

          cs_b_diff_flux_coupling_vector(idiffp,
                                         pipr,
                                         pjpr,
                                         heq,
                                         fluxi);

          for (int k = 0; k < 3; k++)
            rhs[jj][k] -= thetap * fluxi[k];
        }

        BFT_FREE(pvar_local);
        /* Sending structures are no longer needed */
        BFT_FREE(pvar_distant);
        if (df_limiter != NULL) {
          BFT_FREE(df_limiter_local);
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_3_t pip;
            cs_real_3_t _pi;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (b_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(b_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pi);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady_vector(bldfrp,
                                    diipb[face_id],
                                    (const cs_real_3_t *)grad[ii],
                                    _pi,
                                    pip);

            cs_b_upwind_flux_vector(iconvp,
                                    thetap,
                                    imasac,
                                    inc,
                                    bc_type[face_id],
                                    _pi,
                                    _pi, /* no relaxation */
                                    pip,
                                    coefav[face_id],
                                    coefbv[face_id],
                                    b_massflux[face_id],
                                    fluxi);

            cs_b_diff_flux_vector(idiffp,
                                  thetap,
                                  inc,
                                  pip,
                                  cofafv[face_id],
                                  cofbfv[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for(int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            }

          }
        }
      }

      /* The variable is internally coupled and an implicit contribution
       * is required */
      if (icoupl > 0) {
        /* Prepare data for sending */
        BFT_MALLOC(pvar_distant, n_distant, cs_real_3_t);

        for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
          cs_lnum_t face_id = faces_distant[ii];
          cs_lnum_t jj = b_face_cells[face_id];

          cs_real_3_t pip;
          cs_real_3_t _pj;

          for (int i = 0; i < 3; i++) {
            _pj[i]  = _pvar[jj][i];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          /* Note: to be treated exactly as a internal face, should be a bending
           * between the two cells... */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[jj], 0.);

          /* Scaling due to mass balance in porous modelling */
          if (b_f_face_factor != NULL) {
            cs_real_3_t n;
            cs_math_3_normalise(b_face_normal[face_id], n);

            cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pj);
          }

          cs_b_cd_unsteady_vector(bldfrp,
                                  diipb[face_id],
                                  (const cs_real_3_t *)grad[jj],
                                  _pj,
                                  pip);

          for (int k = 0; k < 3; k++)
            pvar_distant[ii][k] = pip[k];
        }

        /* Receive data */
        BFT_MALLOC(pvar_local, n_local, cs_real_3_t);
        cs_internal_coupling_exchange_var(cpl,
                                          3, /* Dimension */
                                          (cs_real_t *)pvar_distant,
                                          (cs_real_t *)pvar_local);

        if (df_limiter != NULL) {
          BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
          cs_internal_coupling_exchange_var(cpl,
                                            1, /* Dimension */
                                            df_limiter,
                                            df_limiter_local);
        }

        /* Flux contribution */
        assert(f != NULL);
        cs_real_t *hintp = f->bc_coeffs->hint;
        cs_real_t *hextp = f->bc_coeffs->hext;
        for (cs_lnum_t ii = 0; ii < n_local; ii++) {
          cs_lnum_t face_id = faces_local[ii];
          cs_lnum_t jj = b_face_cells[face_id];
          cs_real_t pip[3], pjp[3];
          cs_real_t fluxi[3] = {0., 0., 0.};
          cs_real_3_t _pj;

          for (int i = 0; i < 3; i++) {
            _pj[i]  = _pvar[jj][i];
          }

          /* Scaling due to mass balance in porous modelling */
          if (b_f_face_factor != NULL) {
            cs_real_3_t n;
            cs_math_3_normalise(b_face_normal[face_id], n);

            cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pj);
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

          cs_b_cd_unsteady_vector(bldfrp,
                                  diipb[face_id],
                                  (const cs_real_3_t *)grad[jj],
                                  _pj,
                                  pip);

          for (int k = 0; k < 3; k++)
            pjp[k] = pvar_local[ii][k];

          hint = hintp[face_id];
          hext = hextp[face_id];
          heq = hint * hext / (hint + hext);

          cs_b_diff_flux_coupling_vector(idiffp,
                                         pip,
                                         pjp,
                                         heq,
                                         fluxi);

          for (int k = 0; k < 3; k++)
            rhs[jj][k] -= thetap * fluxi[k];
        }

        BFT_FREE(pvar_local);
        /* Sending structures are no longer needed */
        BFT_FREE(pvar_distant);
        if (df_limiter != NULL) {
          BFT_FREE(df_limiter_local);
        }
      }
    } /* idtvar */

    /* Boundary convective flux imposed at some faces (tags in icvfli array) */
  } else if (icvflb == 1) {

    /* Retrieve the value of the convective flux to be imposed */
    if (f_id != -1) {
      coface = (const cs_real_3_t *)(f->bc_coeffs->ac);
      cofbce = (const cs_real_33_t *)(f->bc_coeffs->bc);
    } else {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of icvflb and f_id"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi[3], pir[3], pipr[3];

            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_3_t _pi, _pia;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
              _pia[i] = pvara[ii][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (b_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(b_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pi);
              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pia);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady_vector(bldfrp,
                                  relaxp,
                                  diipb[face_id],
                                  (const cs_real_3_t *)grad[ii],
                                  _pi,
                                  _pia,
                                  pir,
                                  pipr);

            cs_b_imposed_conv_flux_vector(iconvp,
                                          1., /* thetap */
                                          1., /* imasac */
                                          inc,
                                          bc_type[face_id],
                                          icvfli[face_id],
                                          _pvar[ii],
                                          pir,
                                          pipr,
                                          coefav[face_id],
                                          coefbv[face_id],
                                          coface[face_id],
                                          cofbce[face_id],
                                          b_massflux[face_id],
                                          fluxi);

            cs_b_diff_flux_vector(idiffp,
                                  1., /* thetap */
                                  inc,
                                  pipr,
                                  cofafv[face_id],
                                  cofbfv[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            }

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            cs_real_t fluxi[3] ;
            for (int isou =  0; isou < 3; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_3_t pip;
            cs_real_3_t _pi;

            for (int i = 0; i < 3; i++) {
              _pi[i]  = _pvar[ii][i];
            }

            /* Scaling due to mass balance in porous modelling */
            if (b_f_face_factor != NULL) {
              cs_real_3_t n;
              cs_math_3_normalise(b_face_normal[face_id], n);

              cs_math_3_normal_scaling(n, b_f_face_factor[face_id], _pi);
            }

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady_vector(bldfrp,
                                    diipb[face_id],
                                    (const cs_real_3_t *)grad[ii],
                                    _pi,
                                    pip);

            cs_b_imposed_conv_flux_vector(iconvp,
                                          thetap,
                                          imasac,
                                          inc,
                                          bc_type[face_id],
                                          icvfli[face_id],
                                          _pvar[ii],
                                          _pvar[ii], /* no relaxation */
                                          pip,
                                          coefav[face_id],
                                          coefbv[face_id],
                                          coface[face_id],
                                          cofbce[face_id],
                                          b_massflux[face_id],
                                          fluxi);

            cs_b_diff_flux_vector(idiffp,
                                  thetap,
                                  inc,
                                  pip,
                                  cofafv[face_id],
                                  cofbfv[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for (int isou = 0; isou < 3; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            }

          }
        }
      }

    } /* idtvar */

  }

  /* 3. Computation of the transpose grad(vel) term and grad(-2/3 div(vel)) */

  if (ivisep == 1 && idiffp == 1) {

    /* We do not know what condition to put in the inlets and the outlets, so we
       assume that there is an equilibrium. Moreover, cells containing a coupled
       are removed. */

    /* Allocate a temporary array */
    BFT_MALLOC(bndcel, n_cells_ext, cs_real_t);

#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++)
      bndcel[cell_id] = 1.;

#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (cs_lnum_t face_id = 0; face_id < m->n_b_faces; face_id++) {
      int ityp = bc_type[face_id];
      if (   ityp == CS_OUTLET
          || ityp == CS_INLET
          || ityp == CS_FREE_INLET
          || ityp == CS_CONVECTIVE_INLET
          || ityp == CS_COUPLED_FD)
        bndcel[b_face_cells[face_id]] = 0.;
    }

    if (halo != NULL)
      cs_halo_sync_var(halo, halo_type, bndcel);

    /* ---> Interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double pnd = weight[face_id];
          double secvis = i_secvis[face_id]; /* - 2/3 * mu */
          double visco = i_visc[face_id]; /* mu S_ij / d_ij */

          double grdtrv =      pnd*(grad[ii][0][0]+grad[ii][1][1]+grad[ii][2][2])
                 + (1.-pnd)*(grad[jj][0][0]+grad[jj][1][1]+grad[jj][2][2]);

          cs_real_3_t n, ipjp;
          cs_math_3_normalise(i_face_normal[face_id], n);

          /* I'J' */
          for (int i = 0; i < 3; i++)
            ipjp[i] = n[i] * i_dist[face_id];

          /* We need to compute trans_grad(u).I'J' which is equal to I'J'.grad(u) */
          for (int isou = 0; isou < 3; isou++) {

            double tgrdfl = ipjp[0] * (      pnd*grad[ii][0][isou]
                                      + (1.-pnd)*grad[jj][0][isou])
                          + ipjp[1] * (      pnd*grad[ii][1][isou]
                                      + (1.-pnd)*grad[jj][1][isou])
                          + ipjp[2] * (      pnd*grad[ii][2][isou]
                                      + (1.-pnd)*grad[jj][2][isou]);

            double flux = visco*tgrdfl + secvis*grdtrv*i_f_face_normal[face_id][isou];

            rhs[ii][isou] += flux*bndcel[ii];
            rhs[jj][isou] -= flux*bndcel[jj];

          }

        }
      }
    }

    /* ---> Boundary FACES
       the whole flux term of the stress tensor is already taken into account
       (so, no corresponding term in forbr)
       TODO in theory we should take the normal component into account (the
       tangential one is modeled by the wall law) */

#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (cs_lnum_t face_id = 0; face_id < m->n_b_faces; face_id++) {
      cs_lnum_t ii = b_face_cells[face_id];

      /* Trace of velocity gradient */
      double grdtrv = (grad[ii][0][0]+grad[ii][1][1]+grad[ii][2][2]);
      double secvis = b_secvis[face_id]; /* - 2/3 * mu */

      for (int isou = 0; isou < 3; isou++) {

        double flux = secvis*grdtrv*b_f_face_normal[face_id][isou];
        rhs[ii][isou] += flux * bndcel[ii];

      }

    }

    /*Free memory */
    BFT_FREE(bndcel);

  }

  /* Free memory */
  BFT_FREE(grdpa);
  BFT_FREE(grad);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the convection/diffusion terms of a transport
 *  equation of a vector field \f$ \vect{\varia} \f$.
 *
 * More precisely, the right hand side \f$ \vect{Rhs} \f$ is updated as
 * follows:
 * \f[
 *  \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}}      \left(
 *         \dot{m}_\ij \left( \vect{\varia}_\fij - \vect{\varia}_\celli \right)
 *       - \mu_\fij \gradt_\fij \vect{\varia} \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * - \f$ \vect{Rhs} \f$ has already been initialized before calling bilsc!
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     icvflb        global indicator of boundary convection flux
 *                               - 0 upwind scheme at all boundary faces
 *                               - 1 imposed flux at some boundary faces
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     imasac        take mass accumulation into account?
 * \param[in]     pvar          solved velocity (current time step)
 * \param[in]     pvara         solved velocity (previous time step)
 * \param[in]     coefa         boundary condition array for the variable
 *                               (Explicit part)
 * \param[in]     coefb         boundary condition array for the variable
 *                               (Implicit part)
 * \param[in]     cofaf         boundary condition array for the diffusion
 *                               of the variable (Explicit part)
 * \param[in]     cofbf         boundary condition array for the diffusion
 *                               of the variable (Implicit part)
 * \param[in]     i_massflux    mass flux at interior faces
 * \param[in]     b_massflux    mass flux at boundary faces
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_convection_diffusion_tensor(int                         idtvar,
                               int                         f_id,
                               const cs_var_cal_opt_t      var_cal_opt,
                               int                         icvflb,
                               int                         inc,
                               int                         imasac,
                               cs_real_6_t       *restrict pvar,
                               const cs_real_6_t *restrict pvara,
                               const cs_real_6_t           coefa[],
                               const cs_real_66_t          coefb[],
                               const cs_real_6_t           cofaf[],
                               const cs_real_66_t          cofbf[],
                               const cs_real_t             i_massflux[],
                               const cs_real_t             b_massflux[],
                               const cs_real_t             i_visc[],
                               const cs_real_t             b_visc[],
                               cs_real_6_t       *restrict rhs)
{
  const int iconvp = var_cal_opt.iconv;
  const int idiffp = var_cal_opt.idiff;
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int ischcp = var_cal_opt.ischcv;
  const int isstpp = var_cal_opt.isstpc;
  const int iwarnp = var_cal_opt.verbosity;
  const double blencp = var_cal_opt.blencv;
  const double blend_st = var_cal_opt.blend_st;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_face_surf = fvq->i_face_surf;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  cs_real_t *df_limiter = NULL;

  const int *bc_type = cs_glob_bc_type;

  /* Local variables */

  char var_name[64];

  int tr_dim = 0;

  cs_gnum_t n_upwind;
  int iupwin;

  cs_real_63_t *grad, *grdpa;

  cs_field_t *f;

  cs_real_t  *v_slope_test = cs_get_v_slope_test(f_id, var_cal_opt);

  /*==========================================================================*/

  /* 1. Initialization */

  /* Allocate work arrays */

  BFT_MALLOC(grad, n_cells_ext, cs_real_63_t);
  BFT_MALLOC(grdpa, n_cells_ext, cs_real_63_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL && m->halo != NULL) {
    cs_halo_sync_var_strided(m->halo, halo_type, (cs_real_t *)pvar, 6);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(m->halo, halo_type, (cs_real_t *)pvar);
  }
  else if (pvara == NULL)
    pvara = (const cs_real_6_t *restrict)pvar;

  const cs_real_6_t  *restrict _pvar
    = (pvar != NULL) ? (const cs_real_6_t  *restrict)pvar : pvara;

  /* Logging info */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    cs_gradient_perio_init_rij_tensor(&tr_dim, grad);
    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[convection-diffusion, tensor]", 63);
  var_name[63] = '\0';

  if (iwarnp >= 2 && iconvp == 1) {
    if (ischcp == 1) {
      bft_printf
        (
         _(" %s: Convection in centered blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    } else {
      bft_printf
        (
         _(" %s: Convection in 2nd order blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    }
  }

  iupwin = (blencp > 0.) ? 0 : 1;

  /* 2. Compute the balance with reconstruction */

  /* Compute the gradient of the velocity

     The gradient (grad) is used in the flux reconstruction and the slope test.
     Thus we must compute it:
         - when we have diffusion and we reconstruct the fluxes,
         - when the convection scheme is SOLU,
         - when we have convection, we are not in pure upwind
           and we reconstruct the fluxes,
         - when we have convection, we are not in pure upwind
           and we have not shunted the slope test. */

  if (  (idiffp != 0 && ircflp == 1)
     || (   iconvp != 0 && iupwin == 0
         && (ischcp == 0 || ircflp == 1 || isstpp == 0))) {

    cs_gradient_tensor_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    nswrgp,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    coefa,
                                    coefb,
                                    _pvar,
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 6; isou++) {
        for (int jsou = 0; jsou < 3; jsou++)
          grad[cell_id][isou][jsou] = 0.;
      }
    }
  }

  /* ======================================================================
     ---> Compute uncentered gradient grdpa for the slope test
     ======================================================================*/

# pragma omp parallel for
  for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
    for (int jsou = 0; jsou < 3; jsou++) {
      for (int isou = 0; isou < 6; isou++)
        grdpa[cell_id][isou][jsou] = 0.;
    }
  }

  if (iconvp > 0 && iupwin == 0 && isstpp == 0) {

    cs_slope_test_gradient_tensor(inc,
                                  halo_type,
                                  (const cs_real_63_t *)grad,
                                  grdpa,
                                  _pvar,
                                  coefa,
                                  coefb,
                                  i_massflux);

  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  n_upwind = 0;

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 6; isou++)
        rhs[cell_id][isou] = 0.;
    }
  }

  /* --> Pure upwind flux
     =====================*/

  if (iupwin == 1) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }
            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp, pipr, pjpr;
            cs_real_6_t pifri, pifrj, pjfri, pjfrj;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_upwind_tensor(bldfrp,
                                         relaxp,
                                         diipf[face_id],
                                         djjpf[face_id],
                                         (const cs_real_3_t *)grad[ii],
                                         (const cs_real_3_t *)grad[jj],
                                         _pvar[ii],
                                         _pvar[jj],
                                         pvara[ii],
                                         pvara[jj],
                                         pifri,
                                         pifrj,
                                         pjfri,
                                         pjfrj,
                                         pip,
                                         pjp,
                                         pipr,
                                         pjpr);


            cs_i_conv_flux_tensor(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

           for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

    /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }
            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp;
            cs_real_6_t pif, pjf;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_upwind_tensor(bldfrp,
                                           diipf[face_id],
                                           djjpf[face_id],
                                           (const cs_real_3_t *)grad[ii],
                                           (const cs_real_3_t *)grad[jj],
                                           _pvar[ii],
                                           _pvar[jj],
                                           pif,
                                           pjf,
                                           pip,
                                           pjp);

            cs_i_conv_flux_tensor(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 6; isou++) {

              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

    }

    /* --> Flux with no slope test
       ============================*/

  } else if (isstpp == 1) {

    if (ischcp < 0 || ischcp > 1) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcp"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for

        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp, pipr, pjpr;
            cs_real_6_t pifri, pifrj, pjfri, pjfrj;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_tensor(bldfrp,
                                  ischcp,
                                  relaxp,
                                  blencp,
                                  weight[face_id],
                                  cell_cen[ii],
                                  cell_cen[jj],
                                  i_face_cog[face_id],
                                  diipf[face_id],
                                  djjpf[face_id],
                                  (const cs_real_3_t *)grad[ii],
                                  (const cs_real_3_t *)grad[jj],
                                  _pvar[ii],
                                  _pvar[jj],
                                  pvara[ii],
                                  pvara[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr);

            cs_i_conv_flux_tensor(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp;
            cs_real_6_t pif, pjf;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_tensor(bldfrp,
                                    ischcp,
                                    blencp,
                                    weight[face_id],
                                    cell_cen[ii],
                                    cell_cen[jj],
                                    i_face_cog[face_id],
                                    diipf[face_id],
                                    djjpf[face_id],
                                    (const cs_real_3_t *)grad[ii],
                                    (const cs_real_3_t *)grad[jj],
                                    _pvar[ii],
                                    _pvar[jj],
                                    pif,
                                    pjf,
                                    pip,
                                    pjp);

            cs_i_conv_flux_tensor(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }
          }
        }
      }
    }

    /* --> Flux with slope test
       =========================*/

  } else {

    if (ischcp < 0 || ischcp > 1) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcp"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp, pipr, pjpr;
            cs_real_6_t pifri, pifrj, pjfri, pjfrj;
            bool upwind_switch = false;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_slope_test_tensor(&upwind_switch,
                                             iconvp,
                                             bldfrp,
                                             ischcp,
                                             relaxp,
                                             blencp,
                                             blend_st,
                                             weight[face_id],
                                             i_dist[face_id],
                                             i_face_surf[face_id],
                                             cell_cen[ii],
                                             cell_cen[jj],
                                             i_face_normal[face_id],
                                             i_face_cog[face_id],
                                             diipf[face_id],
                                             djjpf[face_id],
                                             i_massflux[face_id],
                                             (const cs_real_3_t *)grad[ii],
                                             (const cs_real_3_t *)grad[jj],
                                             (const cs_real_3_t *)grdpa[ii],
                                             (const cs_real_3_t *)grdpa[jj],
                                             _pvar[ii],
                                             _pvar[jj],
                                             pvara[ii],
                                             pvara[jj],
                                             pifri,
                                             pifrj,
                                             pjfri,
                                             pjfrj,
                                             pip,
                                             pjp,
                                             pipr,
                                             pjpr);

            cs_i_conv_flux_tensor(iconvp,
                                  1.,
                                  1,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pifri,
                                  pifrj,
                                  pjfri,
                                  pjfrj,
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  1.,
                                  pip,
                                  pjp,
                                  pipr,
                                  pjpr,
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            }

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            double fluxi[6], fluxj[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
              fluxj[isou] = 0;
            }
            cs_real_6_t pip, pjp;
            cs_real_6_t pif, pjf;
            bool upwind_switch = false;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_slope_test_tensor(&upwind_switch,
                                               iconvp,
                                               bldfrp,
                                               ischcp,
                                               blencp,
                                               blend_st,
                                               weight[face_id],
                                               i_dist[face_id],
                                               i_face_surf[face_id],
                                               cell_cen[ii],
                                               cell_cen[jj],
                                               i_face_normal[face_id],
                                               i_face_cog[face_id],
                                               diipf[face_id],
                                               djjpf[face_id],
                                               i_massflux[face_id],
                                               (const cs_real_3_t *)grad[ii],
                                               (const cs_real_3_t *)grad[jj],
                                               (const cs_real_3_t *)grdpa[ii],
                                               (const cs_real_3_t *)grdpa[jj],
                                               _pvar[ii],
                                               _pvar[jj],
                                               pif,
                                               pjf,
                                               pip,
                                               pjp);

            cs_i_conv_flux_tensor(iconvp,
                                  thetap,
                                  imasac,
                                  _pvar[ii],
                                  _pvar[jj],
                                  pif,
                                  pif, /* no relaxation */
                                  pjf,
                                  pjf, /* no relaxation */
                                  i_massflux[face_id],
                                  fluxi,
                                  fluxj);


            cs_i_diff_flux_tensor(idiffp,
                                  thetap,
                                  pip,
                                  pjp,
                                  pip, /* no relaxation */
                                  pjp, /* no relaxation */
                                  i_visc[face_id],
                                  fluxi,
                                  fluxj);

            if (upwind_switch) {
              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;

              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }
            }

            for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
              rhs[jj][isou] += fluxj[isou];
            } /* isou */
          }
        }
      }
    } /* idtvar */
  } /* iupwin */

  if (iwarnp >= 2 && iconvp == 1) {

    /* Sum number of clippings */
    cs_parall_counter(&n_upwind, 1);

    bft_printf(_(" %s: %llu Faces with upwind on %llu interior faces \n"),
               var_name, (unsigned long long)n_upwind,
               (unsigned long long)m->n_g_i_c_faces);
  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Boundary convective flux are all computed with an upwind scheme */
  if (icvflb == 0) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            double fluxi[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_6_t pir, pipr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_steady_tensor(bldfrp,
                                  relaxp,
                                  diipb[face_id],
                                  (const cs_real_3_t *)grad[ii],
                                  _pvar[ii],
                                  pvara[ii],
                                  pir,
                                  pipr);

            cs_b_upwind_flux_tensor(iconvp,
                                    1., /* thetap */
                                    1, /* imasac */
                                    inc,
                                    bc_type[face_id],
                                    _pvar[ii],
                                    pir,
                                    pipr,
                                    coefa[face_id],
                                    coefb[face_id],
                                    b_massflux[face_id],
                                    fluxi);

            cs_b_diff_flux_tensor(idiffp,
                                  1., /* thetap */
                                  inc,
                                  pipr,
                                  cofaf[face_id],
                                  cofbf[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for (int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            }
          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_b_groups; g_id++) {
#       pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
        for (int t_id = 0; t_id < n_b_threads; t_id++) {
          for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
               face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = b_face_cells[face_id];

            double fluxi[6] ;
            for (int isou =  0; isou < 6; isou++) {
              fluxi[isou] = 0;
            }
            cs_real_6_t pip;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(df_limiter[ii], 0.);

            cs_b_cd_unsteady_tensor(bldfrp,
                                    diipb[face_id],
                                    (const cs_real_3_t *)grad[ii],
                                    _pvar[ii],
                                    pip);

            cs_b_upwind_flux_tensor(iconvp,
                                    thetap,
                                    imasac,
                                    inc,
                                    bc_type[face_id],
                                    _pvar[ii],
                                    _pvar[ii], /* no relaxation */
                                    pip,
                                    coefa[face_id],
                                    coefb[face_id],
                                    b_massflux[face_id],
                                    fluxi);

            cs_b_diff_flux_tensor(idiffp,
                                  thetap,
                                  inc,
                                  pip,
                                  cofaf[face_id],
                                  cofbf[face_id],
                                  b_visc[face_id],
                                  fluxi);

            for(int isou = 0; isou < 6; isou++) {
              rhs[ii][isou] -= fluxi[isou];
            } /* isou */
          }
        }
      }

    } /* idtvar */

  }

  /* Free memory */
  BFT_FREE(grdpa);
  BFT_FREE(grad);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the convection/diffusion terms of a transport
 * equation of a scalar field \f$ \varia \f$ such as the temperature.
 *
 * More precisely, the right hand side \f$ Rhs \f$ is updated as
 * follows:
 * \f[
 * Rhs = Rhs + \sum_{\fij \in \Facei{\celli}}      \left(
 *        C_p\dot{m}_\ij \varia_\fij
 *      - \lambda_\fij \gradv_\fij \varia \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * \f$ Rhs \f$ has already been initialized before calling bilsct!
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
 *                                 (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     imasac        take mass accumulation into account?
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_massflux    mass flux at interior faces
 * \param[in]     b_massflux    mass flux at boundary faces
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     xcpp          array of specific heat (\f$ C_p \f$)
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_convection_diffusion_thermal(int                       idtvar,
                                int                       f_id,
                                const cs_var_cal_opt_t    var_cal_opt,
                                int                       inc,
                                int                       iccocg,
                                int                       imasac,
                                cs_real_t       *restrict pvar,
                                const cs_real_t *restrict pvara,
                                const cs_real_t           coefap[],
                                const cs_real_t           coefbp[],
                                const cs_real_t           cofafp[],
                                const cs_real_t           cofbfp[],
                                const cs_real_t           i_massflux[],
                                const cs_real_t           b_massflux[],
                                const cs_real_t           i_visc[],
                                const cs_real_t           b_visc[],
                                const cs_real_t           xcpp[],
                                cs_real_t       *restrict rhs)
{
  const int iconvp = var_cal_opt.iconv ;
  const int idiffp = var_cal_opt.idiff ;
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int ischcp = var_cal_opt.ischcv;
  const int isstpp = var_cal_opt.isstpc;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  int limiter_choice = -1;
  const double blencp = var_cal_opt.blencv;
  const double blend_st = var_cal_opt.blend_st;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_face_surf = fvq->i_face_surf;
  const cs_real_t *restrict cell_vol = fvq->cell_vol;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int *bc_type = cs_glob_bc_type;

  /* Local variables */

  char var_name[64];

  cs_gnum_t n_upwind;
  int iupwin;
  int tr_dim = 0;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_3_t *grad;
  cs_real_3_t *gradup = NULL;
  cs_real_3_t *gradst = NULL;
  cs_field_t *f = NULL;

  cs_real_t *local_min = NULL;
  cs_real_t *local_max = NULL;

  cs_real_t *cv_limiter = NULL;
  cs_real_t *df_limiter = NULL;

  cs_real_t *gweight = NULL;

  cs_real_t  *v_slope_test = cs_get_v_slope_test(f_id,  var_cal_opt);

  /* Internal coupling variables */
  cs_real_t *pvar_local = NULL;
  cs_real_t *pvar_distant = NULL;
  cs_real_t *df_limiter_local = NULL;
  cs_real_t hint, hext, heq;
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  cs_lnum_t n_distant;
  cs_lnum_t *faces_distant = NULL;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /*==========================================================================*/

  /* 1. Initialization */

  /* Allocate work arrays */
  BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL)
    cs_sync_scalar_halo(m, tr_dim, pvar);
  else if (pvara == NULL)
    pvara = (const cs_real_t *restrict)pvar;

  const cs_real_t  *restrict _pvar = (pvar != NULL) ? pvar : pvara;

  /* Slope limiters */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);
    /* Get option from the field */
    if (ischcp == 4) {
      const int key_limiter = cs_field_key_id("limiter_choice");
      limiter_choice = cs_field_get_key_int(f, key_limiter);
      BFT_MALLOC(local_max, n_cells_ext, cs_real_t);
      BFT_MALLOC(local_min, n_cells_ext, cs_real_t);
      cs_field_local_extrema_scalar(f_id,
                                    halo_type,
                                    local_max,
                                    local_min);

      assert(limiter_choice < CS_NVD_VOF_HRIC); /* VOF scheme forbidden here */
    }

    int cv_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("convection_limiter_id"));
    if (cv_limiter_id > -1)
      cv_limiter = cs_field_by_id(cv_limiter_id)->val;

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[convection-diffusion, thermal]", 63);
  var_name[63] = '\0';

  if (iwarnp >= 2) {
    if (ischcp == 1) {
      bft_printf
        (
         _(" %s: Convection in centered blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    } else {
      bft_printf
        (
         _(" %s: Convection in 2nd order blending with %f percent of upwind\n"),
         var_name, (1.-blencp)*100.);
    }
  }

  iupwin = (blencp > 0.) ? 0 : 1;

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       &n_distant,
                                       &faces_distant);
  }

  /* 2. Compute the balance with reconstruction technics */

  /* Compute the gradient of the variable

     The gradient (grad) is used in the flux reconstruction and the slope test.
     Thus we must compute it:
         - when we have diffusion and we reconstruct the fluxes,
         - when the convection scheme is SOLU,
         - when we have convection, we are not in pure upwind
           and we reconstruct the fluxes,
         - when we have convection, we are not in pure upwind
           and we have not shunted the slope test. */

  if (   (idiffp != 0 && ircflp == 1)
      || (   iconvp != 0 && iupwin == 0
          && (ischcp == 0 || ircflp == 1 || isstpp == 0))) {

    if (f_id != -1) {
      /* Get the calculation option from the field */
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    0, /* hyd_p_flag */
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    NULL, /* f_ext exterior force */
                                    coefap,
                                    coefbp,
                                    _pvar,
                                    gweight, /* Weighted gradient */
                                    cpl, /* internal coupling */
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      grad[cell_id][0] = 0.;
      grad[cell_id][1] = 0.;
      grad[cell_id][2] = 0.;
    }
  }

  /* ======================================================================
     ---> Compute uncentered gradient gradpa for the slope test
     ======================================================================*/

  /* 2.1 Compute the gradient for convective scheme (the slope test, limiter, SOLU, etc) */

  /* Slope test gradient */
  if (iconvp > 0 && iupwin == 0 && isstpp == 0) {

    BFT_MALLOC(gradst, n_cells_ext, cs_real_3_t);

# pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      gradst[cell_id][0] = 0.;
      gradst[cell_id][1] = 0.;
      gradst[cell_id][2] = 0.;
    }

    cs_slope_test_gradient(f_id,
                           inc,
                           halo_type,
                           (const cs_real_3_t *)grad,
                           gradst,
                           _pvar,
                           coefap,
                           coefbp,
                           i_massflux);

  }

  /* Pure SOLU scheme without using gradient_slope_test function
     or NVD/TVD limiters */
  if (iconvp > 0 && iupwin == 0 && (ischcp == 2 || ischcp == 4)) {

    BFT_MALLOC(gradup, n_cells_ext, cs_real_3_t);

# pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      gradup[cell_id][0] = 0.;
      gradup[cell_id][1] = 0.;
      gradup[cell_id][2] = 0.;
    }

    cs_upwind_gradient(f_id,
                       inc,
                       halo_type,
                       coefap,
                       coefbp,
                       i_massflux,
                       b_massflux,
                       _pvar,
                       gradup);

  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  n_upwind = 0;

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext - n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++)
      rhs[cell_id] = 0.;
  }

  /* --> Pure upwind flux
     =====================*/

  if (iupwin == 1) {

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_upwind(bldfrp,
                                  relaxp,
                                  diipf[face_id],
                                  djjpf[face_id],
                                  grad[ii],
                                  grad[jj],
                                  _pvar[ii],
                                  _pvar[jj],
                                  pvara[ii],
                                  pvara[jj],
                                  &pifri,
                                  &pifrj,
                                  &pjfri,
                                  &pjfrj,
                                  &pip,
                                  &pjp,
                                  &pipr,
                                  &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           xcpp[ii],
                           xcpp[jj],
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            /* in parallel, face will be counted by one and only one rank */
            if (ii < n_cells) {
              n_upwind++;
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_upwind(bldfrp,
                                    diipf[face_id],
                                    djjpf[face_id],
                                    grad[ii],
                                    grad[jj],
                                    _pvar[ii],
                                    _pvar[jj],
                                    &pif,
                                    &pjf,
                                    &pip,
                                    &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           xcpp[ii],
                           xcpp[jj],
                           fluxij);

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip,/* no relaxation */
                           pjp,/* no relaxation */
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    }

  /* --> Flux with no slope test or Min/Max Beta limiter
    ====================================================*/

  } else if (isstpp == 1 || isstpp == 2) {

    if (ischcp < 0 || ischcp > 2) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady(bldfrp,
                           ischcp,
                           relaxp,
                           blencp,
                           weight[face_id],
                           cell_cen[ii],
                           cell_cen[jj],
                           i_face_cog[face_id],
                           diipf[face_id],
                           djjpf[face_id],
                           grad[ii],
                           grad[jj],
                           gradup[ii],
                           gradup[jj],
                           _pvar[ii],
                           _pvar[jj],
                           pvara[ii],
                           pvara[jj],
                           &pifri,
                           &pifrj,
                           &pjfri,
                           &pjfrj,
                           &pip,
                           &pjp,
                           &pipr,
                           &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           xcpp[ii],
                           xcpp[jj],
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_t beta = blencp;

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            /* Beta blending coefficient ensuring the positivity of the scalar */
            if (isstpp == 2) {
              beta = CS_MAX(CS_MIN(cv_limiter[ii], cv_limiter[jj]), 0.);
            }

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_real_t hybrid_coef_ii, hybrid_coef_jj;
            if (ischcp == 3) {
              hybrid_coef_ii = CS_F_(hybrid_blend)->val[ii];
              hybrid_coef_jj = CS_F_(hybrid_blend)->val[jj];

              cs_i_cd_unsteady(bldfrp,
                               ischcp,
                               beta,
                               weight[face_id],
                               cell_cen[ii],
                               cell_cen[jj],
                               i_face_cog[face_id],
                               hybrid_coef_ii,
                               hybrid_coef_jj,
                               diipf[face_id],
                               djjpf[face_id],
                               grad[ii],
                               grad[jj],
                               gradup[ii],
                               gradup[jj],
                               _pvar[ii],
                               _pvar[jj],
                               &pif,
                               &pjf,
                               &pip,
                               &pjp);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             xcpp[ii],
                             xcpp[jj],
                             fluxij);
            } else if (ischcp == 4) {
              /* NVD/TVD family of high accuracy schemes */

              cs_lnum_t ic, id;

              /* Determine central and downwind sides w.r.t. current face */
              cs_central_downwind_cells(ii,
                                        jj,
                                        i_massflux[face_id],
                                        &ic,  /* central cell id */
                                        &id); /* downwind cell id */

              cs_i_cd_unsteady_nvd(limiter_choice,
                                   beta,
                                   cell_cen[ic],
                                   cell_cen[id],
                                   i_face_normal[face_id],
                                   i_face_cog[face_id],
                                   grad[ic],
                                   _pvar[ic],
                                   _pvar[id],
                                   local_max[ic],
                                   local_min[ic],
                                   -1., /* courant */
                                   &pif,
                                   &pjf);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             xcpp[ii],
                             xcpp[jj],
                             fluxij);


              /* Compute required quantities for diffusive flux */
              cs_real_t recoi, recoj;

              cs_i_compute_quantities(bldfrp,
                                      diipf[face_id],
                                      djjpf[face_id],
                                      grad[ii],
                                      grad[jj],
                                      _pvar[ii],
                                      _pvar[jj],
                                      &recoi,
                                      &recoj,
                                      &pip,
                                      &pjp);

            } else {
              hybrid_coef_ii = 0.;
              hybrid_coef_jj = 0.;

              cs_i_cd_unsteady(bldfrp,
                               ischcp,
                               beta,
                               weight[face_id],
                               cell_cen[ii],
                               cell_cen[jj],
                               i_face_cog[face_id],
                               hybrid_coef_ii,
                               hybrid_coef_jj,
                               diipf[face_id],
                               djjpf[face_id],
                               grad[ii],
                               grad[jj],
                               gradup[ii],
                               gradup[jj],
                               _pvar[ii],
                               _pvar[jj],
                               &pif,
                               &pjf,
                               &pip,
                               &pjp);

              cs_i_conv_flux(iconvp,
                             thetap,
                             imasac,
                             _pvar[ii],
                             _pvar[jj],
                             pif,
                             pif, /* no relaxation */
                             pjf,
                             pjf, /* no relaxation */
                             i_massflux[face_id],
                             xcpp[ii],
                             xcpp[jj],
                             fluxij);

            }

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip, /* no relaxation */
                           pjp, /* no relaxation */
                           i_visc[face_id],
                           fluxij);

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    }

  /* --> Flux with slope test
    ============================================*/

  } else {

    if (ischcp < 0 || ischcp > 2) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of ischcv"));
    }
    if (isstpp != 0) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of isstpc"));
    }

    /* Steady */
    if (idtvar < 0) {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_2_t fluxij = {0.,0.};

            cs_real_t pifri, pjfri, pifrj, pjfrj;
            cs_real_t pip, pjp, pipr, pjpr;

            bool upwind_switch = false;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_steady_slope_test(&upwind_switch,
                                      iconvp,
                                      bldfrp,
                                      ischcp,
                                      relaxp,
                                      blencp,
                                      blend_st,
                                      weight[face_id],
                                      i_dist[face_id],
                                      i_face_surf[face_id],
                                      cell_cen[ii],
                                      cell_cen[jj],
                                      i_face_normal[face_id],
                                      i_face_cog[face_id],
                                      diipf[face_id],
                                      djjpf[face_id],
                                      i_massflux[face_id],
                                      grad[ii],
                                      grad[jj],
                                      gradup[ii],
                                      gradup[jj],
                                      gradst[ii],
                                      gradst[jj],
                                      _pvar[ii],
                                      _pvar[jj],
                                      pvara[ii],
                                      pvara[jj],
                                      &pifri,
                                      &pifrj,
                                      &pjfri,
                                      &pjfrj,
                                      &pip,
                                      &pjp,
                                      &pipr,
                                      &pjpr);

            cs_i_conv_flux(iconvp,
                           1.,
                           1,
                           _pvar[ii],
                           _pvar[jj],
                           pifri,
                           pifrj,
                           pjfri,
                           pjfrj,
                           i_massflux[face_id],
                           xcpp[ii],
                           xcpp[jj],
                           fluxij);

            cs_i_diff_flux(idiffp,
                           1.,
                           pip,
                           pjp,
                           pipr,
                           pjpr,
                           i_visc[face_id],
                           fluxij);

            if (upwind_switch) {

              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;
              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }

            }

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

      /* Unsteady */
    } else {

      for (int g_id = 0; g_id < n_i_groups; g_id++) {
#       pragma omp parallel for reduction(+:n_upwind)
        for (int t_id = 0; t_id < n_i_threads; t_id++) {
          for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
               face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
               face_id++) {

            cs_lnum_t ii = i_face_cells[face_id][0];
            cs_lnum_t jj = i_face_cells[face_id][1];

            cs_real_2_t fluxij = {0.,0.};

            bool upwind_switch = false;

            cs_real_t pif, pjf;
            cs_real_t pip, pjp;

            cs_real_t bldfrp = (cs_real_t) ircflp;
            /* Local limitation of the reconstruction */
            if (df_limiter != NULL && ircflp > 0)
              bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

            cs_i_cd_unsteady_slope_test(&upwind_switch,
                                        iconvp,
                                        bldfrp,
                                        ischcp,
                                        blencp,
                                        blend_st,
                                        weight[face_id],
                                        i_dist[face_id],
                                        i_face_surf[face_id],
                                        cell_cen[ii],
                                        cell_cen[jj],
                                        i_face_normal[face_id],
                                        i_face_cog[face_id],
                                        diipf[face_id],
                                        djjpf[face_id],
                                        i_massflux[face_id],
                                        grad[ii],
                                        grad[jj],
                                        gradup[ii],
                                        gradup[jj],
                                        gradst[ii],
                                        gradst[jj],
                                        _pvar[ii],
                                        _pvar[jj],
                                        &pif,
                                        &pjf,
                                        &pip,
                                        &pjp);

            cs_i_conv_flux(iconvp,
                           thetap,
                           imasac,
                           _pvar[ii],
                           _pvar[jj],
                           pif,
                           pif, /* no relaxation */
                           pjf,
                           pjf, /* no relaxation */
                           i_massflux[face_id],
                           xcpp[ii],
                           xcpp[jj],
                           fluxij);

            cs_i_diff_flux(idiffp,
                           thetap,
                           pip,
                           pjp,
                           pip, /* no relaxation */
                           pjp, /* no relaxation */
                           i_visc[face_id],
                           fluxij);

            if (upwind_switch) {

              /* in parallel, face will be counted by one and only one rank */
              if (ii < n_cells)
                n_upwind++;
              if (v_slope_test != NULL) {
                v_slope_test[ii] += fabs(i_massflux[face_id]) / cell_vol[ii];
                v_slope_test[jj] += fabs(i_massflux[face_id]) / cell_vol[jj];
              }

            }

            rhs[ii] -= fluxij[0];
            rhs[jj] += fluxij[1];

          }
        }
      }

    } /* idtvar */

  } /* iupwin */


  if (iwarnp >= 2 && iconvp == 1) {

    /* Sum number of clippings */
    cs_parall_counter(&n_upwind, 1);

    bft_printf(_(" %s: %llu Faces with upwind on %llu interior faces \n"),
               var_name, (unsigned long long)n_upwind,
               (unsigned long long)m->n_g_i_c_faces);
  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t fluxi = 0.;
          cs_real_t pir, pipr;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          cs_b_cd_steady(bldfrp,
                         relaxp,
                         diipb[face_id],
                         grad[ii],
                         _pvar[ii],
                         pvara[ii],
                         &pir,
                         &pipr);

          cs_b_upwind_flux(iconvp,
                           1.,
                           1,
                           inc,
                           bc_type[face_id],
                           _pvar[ii],
                           pir,
                           pipr,
                           coefap[face_id],
                           coefbp[face_id],
                           b_massflux[face_id],
                           xcpp[ii],
                           &fluxi);

          cs_b_diff_flux(idiffp,
                         1., /* thetap */
                         inc,
                         pipr,
                         cofafp[face_id],
                         cofbfp[face_id],
                         b_visc[face_id],
                         &fluxi);

          rhs[ii] -= fluxi;

        }
      }
    }

    /* The thermal is internal_coupled and an implicit contribution
     * is required */
    if (icoupl > 0) {
      /* Prepare data for sending */
      BFT_MALLOC(pvar_distant, n_distant, cs_real_t);

      for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
        cs_lnum_t face_id = faces_distant[ii];
        cs_lnum_t jj = b_face_cells[face_id];
        cs_real_t pip, pipr;

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        /* Note: to be treated exactly as a internal face, should be a bending
         * between the two cells... */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(df_limiter[jj], 0.);

        cs_b_cd_steady(bldfrp,
                       relaxp,
                       diipb[face_id],
                       grad[jj],
                       _pvar[jj],
                       pvara[jj],
                       &pip,
                       &pipr);
        pvar_distant[ii] = pipr;
      }

      /* Receive data */
      BFT_MALLOC(pvar_local, n_local, cs_real_t);
      cs_internal_coupling_exchange_var(cpl,
                                        1, /* Dimension */
                                        pvar_distant,
                                        pvar_local);
      if (df_limiter != NULL) {
        BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          df_limiter,
                                          df_limiter_local);
      }

      /* Flux contribution */
      assert(f_id!=-1); // Otherwise the "f" can't be used
      cs_real_t *hintp = f->bc_coeffs->hint;
      cs_real_t *hextp = f->bc_coeffs->hext;
      for (cs_lnum_t ii = 0; ii < n_local; ii++) {
        cs_lnum_t face_id = faces_local[ii];
        cs_lnum_t jj = b_face_cells[face_id];
        cs_real_t pip, pipr, pjpr;
        cs_real_t fluxi = 0.;

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

        cs_b_cd_steady(bldfrp,
                       relaxp,
                       diipb[face_id],
                       grad[jj],
                       _pvar[jj],
                       pvara[jj],
                       &pip,
                       &pipr);

        pjpr = pvar_local[ii];

        hint = hintp[face_id];
        hext = hextp[face_id];
        heq = hint * hext / (hint + hext);

        cs_b_diff_flux_coupling(idiffp,
                                pipr,
                                pjpr,
                                heq,
                                &fluxi);

        rhs[jj] -= thetap * fluxi;
      }

      BFT_FREE(pvar_local);
      /* Sending structures are no longer needed */
      BFT_FREE(pvar_distant);
      if (df_limiter != NULL)
        BFT_FREE(df_limiter_local);

    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t fluxi = 0.;
          cs_real_t pip;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          cs_b_cd_unsteady(bldfrp,
                           diipb[face_id],
                           grad[ii],
                           _pvar[ii],
                           &pip);

          cs_b_upwind_flux(iconvp,
                           thetap,
                           imasac,
                           inc,
                           bc_type[face_id],
                           _pvar[ii],
                           _pvar[ii], /* no relaxation */
                           pip,
                           coefap[face_id],
                           coefbp[face_id],
                           b_massflux[face_id],
                           xcpp[ii],
                           &fluxi);

          cs_b_diff_flux(idiffp,
                         thetap,
                         inc,
                         pip,
                         cofafp[face_id],
                         cofbfp[face_id],
                         b_visc[face_id],
                         &fluxi);

          rhs[ii] -= fluxi;

        }
      }
    }

    /* The thermal is internal_coupled and an implicit contribution
     * is required */
    if (icoupl > 0) {
      /* Prepare data for sending */
      BFT_MALLOC(pvar_distant, n_distant, cs_real_t);

      for (cs_lnum_t ii = 0; ii < n_distant; ii++) {
        cs_lnum_t face_id = faces_distant[ii];
        cs_lnum_t jj = b_face_cells[face_id];
        cs_real_t pip;

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        /* Note: to be treated exactly as a internal face, should be a bending
         * between the two cells... */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(df_limiter[jj], 0.);

        cs_b_cd_unsteady(bldfrp,
                         diipb[face_id],
                         grad[jj],
                         _pvar[jj],
                         &pip);
        pvar_distant[ii] = pip;
      }

      /* Receive data */
      BFT_MALLOC(pvar_local, n_local, cs_real_t);
      cs_internal_coupling_exchange_var(cpl,
                                        1, /* Dimension */
                                        pvar_distant,
                                        pvar_local);
      if (df_limiter != NULL) {
        BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          df_limiter,
                                          df_limiter_local);
      }

      /* Flux contribution */
      assert(f_id!=-1); // Otherwise the "f" can't be used
      cs_real_t *hintp = f->bc_coeffs->hint;
      cs_real_t *hextp = f->bc_coeffs->hext;
      for (cs_lnum_t ii = 0; ii < n_local; ii++) {
        cs_lnum_t face_id = faces_local[ii];
        cs_lnum_t jj = b_face_cells[face_id];
        cs_real_t pip, pjp;
        cs_real_t fluxi = 0.;

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

        cs_b_cd_unsteady(bldfrp,
                         diipb[face_id],
                         grad[jj],
                         _pvar[jj],
                         &pip);

        pjp = pvar_local[ii];

        hint = hintp[face_id];
        hext = hextp[face_id];
        heq = hint * hext / (hint + hext);

        cs_b_diff_flux_coupling(idiffp,
                                pip,
                                pjp,
                                heq,
                                &fluxi);

        rhs[jj] -= thetap * fluxi;
      }

      BFT_FREE(pvar_local);
      /* Sending structures are no longer needed */
      BFT_FREE(pvar_distant);
      if (df_limiter != NULL)
        BFT_FREE(df_limiter_local);

    }

  }

  /* Free memory */
  BFT_FREE(grad);
  BFT_FREE(gradup);
  BFT_FREE(gradst);
  BFT_FREE(local_max);
  BFT_FREE(local_min);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the diffusion terms with a symmetric tensor
 * diffusivity for a transport equation of a scalar field \f$ \varia \f$.
 *
 * More precisely, the right hand side \f$ Rhs \f$ is updated as
 * follows:
 * \f[
 * Rhs = Rhs - \sum_{\fij \in \Facei{\celli}}      \left(
 *      - \tens{\mu}_\fij \gradv_\fij \varia \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * - \f$ Rhs \f$ has already been initialized before
 *   calling cs_anisotropic_diffusion_scalar!
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
                                (for iterativ gradients)
 *                               - 0 otherwise
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     viscel        symmetric cell tensor \f$ \tens{\mu}_\celli \f$
 * \param[in]     weighf        internal face weight between cells i j in case
 *                               of tensor diffusion
 * \param[in]     weighb        boundary face weight for cells i in case
 *                               of tensor diffusion
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_anisotropic_diffusion_scalar(int                       idtvar,
                                int                       f_id,
                                const cs_var_cal_opt_t    var_cal_opt,
                                int                       inc,
                                int                       iccocg,
                                cs_real_t       *restrict pvar,
                                const cs_real_t *restrict pvara,
                                const cs_real_t           coefap[],
                                const cs_real_t           coefbp[],
                                const cs_real_t           cofafp[],
                                const cs_real_t           cofbfp[],
                                const cs_real_t           i_visc[],
                                const cs_real_t           b_visc[],
                                cs_real_6_t     *restrict viscel,
                                const cs_real_2_t         weighf[],
                                const cs_real_t           weighb[],
                                cs_real_t       *restrict rhs)
{
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];

  int tr_dim = 0;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_6_t *viscce;
  cs_real_6_t *w2;
  cs_real_3_t *grad;

  cs_field_t *f = NULL;

  cs_real_t *gweight = NULL;

  /* Internal coupling variables */
  cs_real_t *pvar_local = NULL;
  cs_real_3_t *grad_local = NULL;
  cs_real_t *df_limiter_local = NULL;
  cs_real_6_t *viscce_local = NULL;
  cs_real_t *weighb_local = NULL;
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /* 1. Initialization */

  viscce = NULL;
  w2 = NULL;

  /* Allocate work arrays */
  BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

  /* Choose gradient type */
  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL)
    cs_sync_scalar_halo(m, tr_dim, pvar);
  else if (pvara == NULL)
    pvara = (const cs_real_t *restrict)pvar;

  const cs_real_t  *restrict _pvar = (pvar != NULL) ? pvar : pvara;

  /* Logging */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[anisotropic diffusion, scalar]", 63);
  var_name[63] = '\0';

  /* Porosity fields */
  cs_field_t *fporo = cs_field_by_name_try("porosity");
  cs_field_t *ftporo = cs_field_by_name_try("tensorial_porosity");

  cs_real_t *porosi = NULL;
  cs_real_6_t *porosf = NULL;

  if (cs_glob_porous_model == 1 || cs_glob_porous_model == 2) {
    porosi = fporo->val;
    if (ftporo != NULL) {
      porosf = (cs_real_6_t *)ftporo->val;
    }
  }

  /* Without porosity */
  if (porosi == NULL) {
    viscce = viscel;

    /* With porosity */
  } else if (porosi != NULL && porosf == NULL) {
    BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
    for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
      for (int isou = 0; isou < 6; isou++) {
        w2[cell_id][isou] = porosi[cell_id]*viscel[cell_id][isou];
      }
    }
    viscce = w2;

    /* With tensorial porosity */
  } else if (porosi != NULL && porosf != NULL) {
    BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
    for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
      cs_math_sym_33_product(porosf[cell_id],
                             viscel[cell_id],
                             w2[cell_id]);
    }
    viscce = w2;
  }

  /* ---> Periodicity and parallelism treatment of symmetric tensors */
  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)viscce, 6);
    if (m->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(halo, halo_type, (cs_real_t *)viscce);
  }

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       NULL,
                                       NULL);
  }

  /* 2. Compute the diffusive part with reconstruction technics */

  /* ======================================================================
     ---> Compute the gradient of the current variable if needed
     ======================================================================*/

  if (ircflp == 1) {

    if (f_id != -1) {
      /* Get the calculation option from the field */
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idifft > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    0, /* hyd_p_flag */
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    NULL, /* f_ext exterior force */
                                    coefap,
                                    coefbp,
                                    _pvar,
                                    gweight, /* Weighted gradient */
                                    cpl, /* internal coupling */
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      grad[cell_id][0] = 0.;
      grad[cell_id][1] = 0.;
      grad[cell_id][2] = 0.;
    }
  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext - n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      rhs[cell_id] = 0.;
    }
  }

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t pi = _pvar[ii];
          cs_real_t pj = _pvar[jj];
          cs_real_t pia = pvara[ii];
          cs_real_t pja = pvara[jj];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /* Recompute II" and JJ"
             ----------------------*/

          cs_real_t visci[3][3], viscj[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          cs_real_t diippf[3], djjppf[3];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          /* p in I" and J" */
          cs_real_t pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                        + grad[ii][1]*diippf[1]
                                        + grad[ii][2]*diippf[2]);
          cs_real_t pjpp = pj + bldfrp*(  grad[jj][0]*djjppf[0]
                                        + grad[jj][1]*djjppf[1]
                                        + grad[jj][2]*djjppf[2]);

          cs_real_t pir = pi/relaxp - (1.-relaxp)/relaxp * pia;
          cs_real_t pjr = pj/relaxp - (1.-relaxp)/relaxp * pja;

          /* pr in I" and J" */
          cs_real_t pippr = pir + bldfrp*(  grad[ii][0]*diippf[0]
                                          + grad[ii][1]*diippf[1]
                                          + grad[ii][2]*diippf[2]);
          cs_real_t pjppr = pjr + bldfrp*(  grad[jj][0]*djjppf[0]
                                          + grad[jj][1]*djjppf[1]
                                          + grad[jj][2]*djjppf[2]);


          cs_real_t fluxi = i_visc[face_id]*(pippr - pjpp);
          cs_real_t fluxj = i_visc[face_id]*(pipp - pjppr);

          rhs[ii] -= fluxi;
          rhs[jj] += fluxj;

        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t pi = _pvar[ii];
          cs_real_t pj = _pvar[jj];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[jj], 0.);

          /* Recompute II" and JJ"
             ----------------------*/

          cs_real_t visci[3][3], viscj[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          cs_real_t diippf[3], djjppf[3];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          /* p in I" and J" */
          cs_real_t pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                        + grad[ii][1]*diippf[1]
                                        + grad[ii][2]*diippf[2]);
          cs_real_t pjpp = pj + bldfrp*(  grad[jj][0]*djjppf[0]
                                        + grad[jj][1]*djjppf[1]
                                        + grad[jj][2]*djjppf[2]);

          cs_real_t flux = i_visc[face_id]*(pipp -pjpp);

          rhs[ii] -= thetap*flux;
          rhs[jj] += thetap*flux;

        }
      }
    }
  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t pi = _pvar[ii];
          cs_real_t pia = pvara[ii];

          cs_real_t pir = pi/relaxp - (1.-relaxp)/relaxp*pia;

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          cs_real_t visci[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          cs_real_t diippf[3];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2] );
          }

          cs_real_t pippr = pir + bldfrp*(  grad[ii][0]*diippf[0]
                                          + grad[ii][1]*diippf[1]
                                          + grad[ii][2]*diippf[2]);

          cs_real_t pfacd = inc*cofafp[face_id] + cofbfp[face_id]*pippr;

          cs_real_t flux = b_visc[face_id]*pfacd;
          rhs[ii] -= flux;

        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t pi = _pvar[ii];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          cs_real_t visci[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          cs_real_t diippf[3];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2]);
          }

          cs_real_t pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                        + grad[ii][1]*diippf[1]
                                        + grad[ii][2]*diippf[2]);

          cs_real_t pfacd = inc*cofafp[face_id] + cofbfp[face_id]*pipp;

          cs_real_t flux = b_visc[face_id]*pfacd;
          rhs[ii] -= thetap*flux;

        }
      }
    }

    /* The scalar is internal_coupled and an implicit contribution
     * is required */
    if (icoupl > 0) {

      /* Exchange pvar */
      BFT_MALLOC(pvar_local, n_local, cs_real_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               1, /* Dimension */
                                               _pvar,
                                               pvar_local);

      /* Exchange grad */
      BFT_MALLOC(grad_local, n_local, cs_real_3_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               3, /* Dimension */
                                               (const cs_real_t*)grad,
                                               (cs_real_t *)grad_local);

      /* Exchange viscce */
      BFT_MALLOC(viscce_local, n_local, cs_real_6_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               6, /* Dimension */
                                               (const cs_real_t*)viscce,
                                               (cs_real_t *)viscce_local);

      /* Exchange weighb */
      BFT_MALLOC(weighb_local, n_local, cs_real_t);
      cs_internal_coupling_exchange_by_face_id(cpl,
                                               1, /* Dimension */
                                               (const cs_real_t*)weighb,
                                               (cs_real_t *)weighb_local);

      /* Exchange diffusion limiter */
      if (df_limiter != NULL) {
        BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          df_limiter,
                                          df_limiter_local);
      }

      /* Flux contribution */
      for (cs_lnum_t jj = 0; jj < n_local; jj++) {
        cs_lnum_t face_id = faces_local[jj];
        cs_lnum_t ii = b_face_cells[face_id];

        cs_real_t pi = _pvar[ii];
        cs_real_t pj = pvar_local[jj];

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

        /* Recompute II" and JJ" */
        cs_real_t visci[3][3], viscj[3][3];
        cs_real_t diippf[3], djjppf[3];

        visci[0][0] = viscce[ii][0];
        visci[1][1] = viscce[ii][1];
        visci[2][2] = viscce[ii][2];
        visci[1][0] = viscce[ii][3];
        visci[0][1] = viscce[ii][3];
        visci[2][1] = viscce[ii][4];
        visci[1][2] = viscce[ii][4];
        visci[2][0] = viscce[ii][5];
        visci[0][2] = viscce[ii][5];

        /* IF.Ki.S / ||Ki.S||^2 */
        cs_real_t fikdvi = weighb[face_id];

        /* II" = IF + FI" */
        for (int i = 0; i < 3; i++) {
          diippf[i] = b_face_cog[face_id][i]-cell_cen[ii][i]
                    - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                             + visci[1][i]*b_face_normal[face_id][1]
                             + visci[2][i]*b_face_normal[face_id][2] );
        }

        viscj[0][0] = viscce_local[jj][0];
        viscj[1][1] = viscce_local[jj][1];
        viscj[2][2] = viscce_local[jj][2];
        viscj[1][0] = viscce_local[jj][3];
        viscj[0][1] = viscce_local[jj][3];
        viscj[2][1] = viscce_local[jj][4];
        viscj[1][2] = viscce_local[jj][4];
        viscj[2][0] = viscce_local[jj][5];
        viscj[0][2] = viscce_local[jj][5];

        /* FJ.Kj.S / ||Kj.S||^2
         * weighb_local defined with vector JF and surface -S */
        cs_real_t fjkdvi = weighb_local[jj];

        /* JJ" = JF + FJ"
         *   */
        for (int i = 0; i < 3; i++) {
          djjppf[i] = b_face_cog[face_id][i]-cell_cen[ii][i]-cpl->ci_cj_vect[jj][i]
                    + fjkdvi*( viscj[0][i]*b_face_normal[face_id][0]
                             + viscj[1][i]*b_face_normal[face_id][1]
                             + viscj[2][i]*b_face_normal[face_id][2] );
        }

        /* p in I" and J" */
        cs_real_t pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                      + grad[ii][1]*diippf[1]
                                      + grad[ii][2]*diippf[2]);
        cs_real_t pjpp = pj + bldfrp*(  grad_local[jj][0]*djjppf[0]
                                      + grad_local[jj][1]*djjppf[1]
                                      + grad_local[jj][2]*djjppf[2]);

        /* Reproduce multiplication by i_visc[face_id] */
        cs_real_t flux = (pipp - pjpp) / (weighb[face_id] + weighb_local[jj]);

        rhs[ii] -= thetap*flux;

      }

      /* Remote data no longer needed */
      BFT_FREE(pvar_local);
      if (df_limiter != NULL)
        BFT_FREE(df_limiter_local);
      BFT_FREE(grad_local);
      BFT_FREE(viscce_local);
      BFT_FREE(weighb_local);
    }

  }

  /* Free memory */
  BFT_FREE(grad);
  BFT_FREE(w2);
}

/*-----------------------------------------------------------------------------*/
/*!
 * \brief Add explicit part of the terms of diffusion by a left-multiplying
 * symmetric tensorial diffusivity for a transport equation of a vector field
 * \f$ \vect{\varia} \f$.
 *
 * More precisely, the right hand side \f$ \vect{Rhs} \f$ is updated as
 * follows:
 * \f[
 * \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}}      \left(
 *      - \gradt_\fij \vect{\varia} \tens{\mu}_\fij  \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Remark:
 * if ivisep = 1, then we also take \f$ \mu \transpose{\gradt\vect{\varia}}
 * + \lambda \trace{\gradt\vect{\varia}} \f$, where \f$ \lambda \f$ is
 * the secondary viscosity, i.e. usually \f$ -\frac{2}{3} \mu \f$.
 *
 * Warning:
 * - \f$ \vect{Rhs} \f$ has already been initialized before calling the present
 *   function
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     ivisep        indicator to take \f$ \divv
 *                               \left(\mu \gradt \transpose{\vect{a}} \right)
 *                               -2/3 \grad\left( \mu \dive \vect{a} \right)\f$
 *                               - 1 take into account,
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     coefav        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbv        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafv        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfv        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \tens{\mu}_\fij \dfrac{S_\fij}{\ipf\jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     i_secvis      secondary viscosity at interior faces
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_anisotropic_left_diffusion_vector(int                         idtvar,
                                     int                         f_id,
                                     const cs_var_cal_opt_t      var_cal_opt,
                                     int                         inc,
                                     int                         ivisep,
                                     cs_real_3_t       *restrict pvar,
                                     const cs_real_3_t *restrict pvara,
                                     const cs_real_3_t           coefav[],
                                     const cs_real_33_t          coefbv[],
                                     const cs_real_3_t           cofafv[],
                                     const cs_real_33_t          cofbfv[],
                                     const cs_real_33_t          i_visc[],
                                     const cs_real_t             b_visc[],
                                     const cs_real_t             i_secvis[],
                                     cs_real_3_t       *restrict rhs)
{
  const int nswrgp = var_cal_opt.nswrgr;
  const int idiffp = var_cal_opt.idiff;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict weight = fvq->weight;
  const cs_real_3_t *restrict i_f_face_normal
    = (const cs_real_3_t *restrict)fvq->i_f_face_normal;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  const int *bc_type = cs_glob_bc_type;

  /* Internal coupling variables */
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  cs_lnum_t n_distant;
  cs_lnum_t *faces_distant = NULL;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];

  cs_real_33_t *gradv;
  cs_real_t *bndcel;

  cs_field_t *f = NULL;

  /* 1. Initialization */

  /* Allocate work arrays */
  BFT_MALLOC(gradv, n_cells_ext, cs_real_33_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL && halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)pvar, 3);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_vect(halo, halo_type, (cs_real_t *)pvar, 3);
  }
  else if (pvara == NULL)
    pvara = (const cs_real_3_t *restrict)pvar;

  const cs_real_3_t  *restrict _pvar
    = (pvar != NULL) ? (const cs_real_3_t  *restrict)pvar : pvara;

  /* logging info */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[anisotropic left diffusion, vector]", 63);
  var_name[63] = '\0';

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       &n_distant,
                                       &faces_distant);
  }


  /* 2. Compute the diffusive part with reconstruction technics */

  /* Compute the gradient of the current variable if needed */

  if (ircflp == 1 || ivisep == 1) {

    cs_gradient_vector_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    nswrgp,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    coefav,
                                    coefbv,
                                    _pvar,
                                    NULL, /* weighted gradient */
                                    cpl,
                                    gradv);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++) {
        for (int jsou = 0; jsou < 3; jsou++)
          gradv[cell_id][isou][jsou] = 0.;
      }
    }
  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext -n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++) {
        rhs[cell_id][isou] = 0.;
      }
    }
  }

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t pip[3], pjp[3], pipr[3], pjpr[3];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /*-----------------
            X-Y-Z components, p = u, v, w */
          for (int isou = 0; isou < 3; isou++) {

            cs_real_t dpvf[3];

            for (int jsou = 0; jsou < 3; jsou++) {
              dpvf[jsou] = 0.5*(gradv[ii][isou][jsou] + gradv[jj][isou][jsou]);
            }

            cs_real_t pi  = _pvar[ii][isou];
            cs_real_t pj  = _pvar[jj][isou];

            cs_real_t pia = pvara[ii][isou];
            cs_real_t pja = pvara[jj][isou];

            /* reconstruction only if IRCFLP = 1 */
            pip[isou] = pi + bldfrp * (cs_math_3_dot_product(dpvf, diipf[face_id]));
            pjp[isou] = pj + bldfrp * (cs_math_3_dot_product(dpvf, djjpf[face_id]));

            pipr[isou] = pi /relaxp - (1.-relaxp)/relaxp * pia
                         + bldfrp * (cs_math_3_dot_product(dpvf, diipf[face_id]));
            pjpr[isou] = pj /relaxp - (1.-relaxp)/relaxp * pja
                         + bldfrp * (cs_math_3_dot_product(dpvf, djjpf[face_id]));

          }

          for (int isou = 0; isou < 3; isou++) {

            cs_real_t fluxi =   i_visc[face_id][0][isou]*(pipr[0] - pjp[0])
                              + i_visc[face_id][1][isou]*(pipr[1] - pjp[1])
                              + i_visc[face_id][2][isou]*(pipr[2] - pjp[2]);
            cs_real_t fluxj =   i_visc[face_id][0][isou]*(pip[0] - pjpr[0])
                              + i_visc[face_id][1][isou]*(pip[1] - pjpr[1])
                              + i_visc[face_id][2][isou]*(pip[2] - pjpr[2]);

            rhs[ii][isou] = rhs[ii][isou] - fluxi;
            rhs[jj][isou] = rhs[jj][isou] + fluxj;

          }

        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t pip[3], pjp[3];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /*-----------------
            X-Y-Z components, p = u, v, w */
          for (int isou = 0; isou < 3; isou++) {

            cs_real_t dpvf[3];

            for (int jsou = 0; jsou < 3; jsou++) {
              dpvf[jsou] = 0.5*(gradv[ii][isou][jsou] + gradv[jj][isou][jsou]);
            }

            cs_real_t pi = _pvar[ii][isou];
            cs_real_t pj = _pvar[jj][isou];

            pip[isou] = pi + bldfrp * (cs_math_3_dot_product(dpvf, diipf[face_id]));
            pjp[isou] = pj + bldfrp * (cs_math_3_dot_product(dpvf, djjpf[face_id]));

          }

          for (int isou = 0; isou < 3; isou++) {

            cs_real_t flux =   i_visc[face_id][0][isou]*(pip[0] - pjp[0])
                             + i_visc[face_id][1][isou]*(pip[1] - pjp[1])
                             + i_visc[face_id][2][isou]*(pip[2] - pjp[2]);

            rhs[ii][isou] -= thetap*flux;
            rhs[jj][isou] += thetap*flux;

          }

        }
      }
    }

  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t cell_id = b_face_cells[face_id];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[cell_id], 0.);

          const cs_real_t *diipbv = diipb[face_id];
          cs_real_t pipr[3];

          for (int k = 0; k < 3; k++) {
            cs_real_t pir  =   _pvar[cell_id][k]/relaxp
                             - (1.-relaxp)/relaxp*pvara[cell_id][k];

            pipr[k] = pir +bldfrp*(  gradv[cell_id][k][0]*diipbv[0]
                                   + gradv[cell_id][k][1]*diipbv[1]
                                   + gradv[cell_id][k][2]*diipbv[2]);

          }

          /*-----------------
            X-Y-Z components, p = u, v, w */
          for (int i = 0; i < 3; i++) {

            cs_real_t pfacd = inc*cofafv[face_id][i];

            /*coefu and cofuf and b_visc are matrices */
            for (int j = 0; j < 3; j++) {

              pfacd += cofbfv[face_id][i][j]*pipr[j];
            }

            rhs[cell_id][i] -= b_visc[face_id] * pfacd;

          } /* i */

        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t cell_id = b_face_cells[face_id];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[cell_id], 0.);

          cs_real_t diipbv[3];

          for (int k = 0; k < 3; k++)
            diipbv[k] = diipb[face_id][k];

          /*-----------------
            X-Y-Z components, p = u, v, w */
          for (int i = 0; i < 3; i++) {

            cs_real_t pfacd = inc*cofafv[face_id][i];

            /*coefu and cofuf are matrices */
            for (int j = 0; j < 3; j++) {
              cs_real_t pir =   _pvar[cell_id][j]
                              + bldfrp*(  gradv[cell_id][j][0]*diipbv[0]
                                        + gradv[cell_id][j][1]*diipbv[1]
                                        + gradv[cell_id][j][2]*diipbv[2]);
              pfacd += cofbfv[face_id][j][i]*pir;
            }

            rhs[cell_id][i] -= thetap * b_visc[face_id] * pfacd;

          } /* i */

        }
      }
    }

  } /* idtvar */

  /* 3. Computation of the transpose grad(vel) term and grad(-2/3 div(vel)) */

  if (ivisep == 1 && idiffp == 1) {

    /* We do not know what condition to put in the inlets and the outlets, so we
       assume that there is an equilibrium. Moreover, cells containing a coupled
       are removed. */

    /* Allocate a temporary array */
    BFT_MALLOC(bndcel, n_cells_ext, cs_real_t);

#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      bndcel[cell_id] = 1.;
    }

#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (cs_lnum_t face_id = 0; face_id < m->n_b_faces; face_id++) {
      int ityp = bc_type[face_id];
      if (   ityp == CS_OUTLET
          || ityp == CS_INLET
          || ityp == CS_FREE_INLET
          || ityp == CS_CONVECTIVE_INLET
          || ityp == CS_COUPLED_FD) {
        bndcel[b_face_cells[face_id]] = 0.;
      }
    }

    if (halo != NULL)
      cs_halo_sync_var(halo, halo_type, bndcel);

    /* ---> Interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t pnd = weight[face_id];
          cs_real_t secvis = i_secvis[face_id];

          cs_real_t grdtrv
            =        pnd*(gradv[ii][0][0]+gradv[ii][1][1]+gradv[ii][2][2])
              + (1.-pnd)*(gradv[jj][0][0]+gradv[jj][1][1]+gradv[jj][2][2]);

          cs_real_3_t n, ipjp;
          cs_math_3_normalise(i_face_normal[face_id], n);

          /* I'J' */
          for (int i = 0; i < 3; i++)
            ipjp[i] = n[i] * i_dist[face_id];

          for (int i = 0; i < 3; i++) {

            cs_real_t flux = secvis*grdtrv*i_f_face_normal[face_id][i];

            /* We need to compute (K grad(u)^T) .I'J'
               which is equal to I'J' . (grad(u) . K^T)
               But: (I'J' . (grad(u) . K^T))_i = I'J'_k grad(u)_kj K_ij
            */

            for (int j = 0; j < 3; j++) {
              for (int k = 0; k < 3; k++) {
                flux += ipjp[k]
                            *(pnd*gradv[ii][k][j]+(1-pnd)*gradv[jj][k][j])
                            *i_visc[face_id][i][j];
              }
            }

            rhs[ii][i] += flux*bndcel[ii];
            rhs[jj][i] -= flux*bndcel[jj];

          }

        }
      }
    }

    /* ---> Boundary FACES
       the whole flux term of the stress tensor is already taken into account
       (so, no corresponding term in forbr)
       TODO in theory we should take the normal component into account (the
       tangential one is modeled by the wall law) */

    /*Free memory */
    BFT_FREE(bndcel);

  }

  /* Free memory */
  BFT_FREE(gradv);
}

/*-----------------------------------------------------------------------------*/
/*!
 * \brief Add explicit part of the terms of diffusion by a right-multiplying
 * symmetric tensorial diffusivity for a transport equation of a vector field
 * \f$ \vect{\varia} \f$.
 *
 * More precisely, the right hand side \f$ \vect{Rhs} \f$ is updated as
 * follows:
 * \f[
 * \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}}      \left(
 *      - \gradt_\fij \vect{\varia} \tens{\mu}_\fij  \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * - \f$ \vect{Rhs} \f$ has already been initialized before calling the present
 *   function
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     coefav        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbv        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafv        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfv        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \tens{\mu}_\fij \dfrac{S_\fij}{\ipf\jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     viscel        symmetric cell tensor \f$ \tens{\mu}_\celli \f$
 * \param[in]     weighf        internal face weight between cells i j in case
 *                               of tensor diffusion
 * \param[in]     weighb        boundary face weight for cells i in case
 *                               of tensor diffusion
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_anisotropic_right_diffusion_vector(int                         idtvar,
                                      int                         f_id,
                                      const cs_var_cal_opt_t      var_cal_opt,
                                      int                         inc,
                                      cs_real_3_t       *restrict pvar,
                                      const cs_real_3_t *restrict pvara,
                                      const cs_real_3_t           coefav[],
                                      const cs_real_33_t          coefbv[],
                                      const cs_real_3_t           cofafv[],
                                      const cs_real_33_t          cofbfv[],
                                      const cs_real_t             i_visc[],
                                      const cs_real_t             b_visc[],
                                      cs_real_6_t     *restrict   viscel,
                                      const cs_real_2_t           weighf[],
                                      const cs_real_t             weighb[],
                                      cs_real_3_t       *restrict rhs)
{
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int iwarnp = var_cal_opt.verbosity;
  const int icoupl = var_cal_opt.icoupl;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;

  /* Internal coupling variables */
  cs_real_3_t *pvar_local = NULL;
  cs_real_33_t *grad_local = NULL;
  cs_real_t *df_limiter_local = NULL;
  cs_real_6_t *viscce_local = NULL;
  cs_real_t *weighb_local = NULL;
  cs_lnum_t *faces_local = NULL;
  cs_lnum_t n_local;
  cs_lnum_t n_distant;
  cs_lnum_t *faces_distant = NULL;
  int coupling_id;
  cs_internal_coupling_t *cpl = NULL;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];

  cs_real_6_t *viscce;
  cs_real_33_t *grad;

  cs_field_t *f = NULL;

  /* 1. Initialization */

  viscce = NULL;

  /* Allocate work arrays */
  BFT_MALLOC(grad, n_cells_ext, cs_real_33_t);

  /* Choose gradient type */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL && halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)pvar, 3);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_vect(halo, halo_type, (cs_real_t *)pvar, 3);
  }
  else if (pvara == NULL)
    pvara = (const cs_real_3_t *restrict)pvar;

  const cs_real_3_t  *restrict _pvar
    = (pvar != NULL) ? (const cs_real_3_t  *restrict)pvar : pvara;

  /* logging info */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[anisotropic right diffusion, vector]", 63);
  var_name[63] = '\0';

  viscce = viscel;

  if (icoupl > 0) {
    assert(f_id != -1);
    const int coupling_key_id = cs_field_key_id("coupling_entity");
    coupling_id = cs_field_get_key_int(f, coupling_key_id);
    cpl = cs_internal_coupling_by_id(coupling_id);
    cs_internal_coupling_coupled_faces(cpl,
                                       &n_local,
                                       &faces_local,
                                       &n_distant,
                                       &faces_distant);
  }

  /* 2. Compute the diffusive part with reconstruction technics */

  /* Compute the gradient of the current variable if needed */

  if (ircflp == 1) {

    cs_gradient_vector_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    nswrgp,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    coefav,
                                    coefbv,
                                    _pvar,
                                    NULL, /* weighted gradient */
                                    cpl,
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++) {
        for (int jsou = 0; jsou < 3; jsou++)
          grad[cell_id][isou][jsou] = 0.;
      }
    }
  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext -n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 3; isou++) {
        rhs[cell_id][isou] = 0.;
      }
    }
  }

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t visci[3][3], viscj[3][3];
          cs_real_t diippf[3], djjppf[3], pipp[3], pjpp[3];
          cs_real_t  pir[3], pjr[3], pippr[3], pjppr[3];
          cs_real_t  pi[3], pj[3], pia[3], pja[3];

          for (int isou = 0; isou < 3; isou++) {
            pi[isou] = _pvar[ii][isou];
            pj[isou] = _pvar[jj][isou];
            pia[isou] = pvara[ii][isou];
            pja[isou] = pvara[jj][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /* Recompute II' and JJ' at this level */

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          for (int isou = 0; isou < 3; isou++) {
            /* p in I" and J" */
            pipp[isou] = pi[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                           + grad[ii][isou][1]*diippf[1]
                                           + grad[ii][isou][2]*diippf[2]);
            pjpp[isou] = pj[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                           + grad[jj][isou][1]*djjppf[1]
                                           + grad[jj][isou][2]*djjppf[2]);

            pir[isou] = pi[isou]/relaxp - (1.-relaxp)/relaxp * pia[isou];
            pjr[isou] = pj[isou]/relaxp - (1.-relaxp)/relaxp * pja[isou];


            /* pr in I" and J" */
            pippr[isou] = pir[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                             + grad[ii][isou][1]*diippf[1]
                                             + grad[ii][isou][2]*diippf[2]);
            pjppr[isou] = pjr[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                             + grad[jj][isou][1]*djjppf[1]
                                             + grad[jj][isou][2]*djjppf[2]);

            cs_real_t fluxi = i_visc[face_id]*(pippr[isou] - pjpp[isou]);
            cs_real_t fluxj = i_visc[face_id]*(pipp[isou] - pjppr[isou]);

            rhs[ii][isou] -= fluxi;
            rhs[jj][isou] += fluxj;
          }
        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t visci[3][3], viscj[3][3];
          cs_real_t diippf[3], djjppf[3], pipp[3], pjpp[3];
          cs_real_t pi[3], pj[3];

          for (int isou = 0; isou < 3; isou++) {
            pi[isou] = _pvar[ii][isou];
            pj[isou] = _pvar[jj][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /* Recompute II' and JJ' at this level */

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          for (int isou = 0; isou < 3; isou++) {
            /* p in I" and J" */
            pipp[isou] = pi[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                           + grad[ii][isou][1]*diippf[1]
                                           + grad[ii][isou][2]*diippf[2]);
            pjpp[isou] = pj[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                           + grad[jj][isou][1]*djjppf[1]
                                           + grad[jj][isou][2]*djjppf[2]);

            cs_real_t flux = i_visc[face_id]*(pipp[isou] -pjpp[isou]);

            rhs[ii][isou] -= thetap*flux;
            rhs[jj][isou] += thetap*flux;

          }

        }
      }
    }

  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t pi[3], pia[3], pir[3], pippr[3];
          cs_real_t visci[3][3];
          cs_real_t diippf[3];

          for (int isou = 0; isou < 3; isou++) {
            pi[isou] = pvar[ii][isou];
            pia[isou] = pvara[ii][isou];
            pir[isou] = pi[isou]/relaxp - (1.-relaxp)/relaxp*pia[isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2] );
          }
          for (int isou = 0; isou < 3; isou++) {
            pippr[isou] = pir[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                             + grad[ii][isou][1]*diippf[1]
                                             + grad[ii][isou][2]*diippf[2]);
          }
          for (int isou = 0; isou < 3; isou++) {
            cs_real_t pfacd = inc*cofafv[face_id][isou];
            for (int jsou = 0; jsou < 3; jsou++) {
              pfacd += cofbfv[face_id][isou][jsou]*pippr[jsou];
            }

            cs_real_t flux = b_visc[face_id]*pfacd;
            rhs[ii][isou] -= flux;

          } /* isou */

        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t visci[3][3];
          cs_real_t diippf[3], pi[3], pipp[3];

          for (int isou = 0; isou < 3; isou++) {
            pi[isou] = pvar[ii][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2]);
          }
          for (int isou = 0; isou < 3; isou++) {
            pipp[isou] = pi[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                           + grad[ii][isou][1]*diippf[1]
                                           + grad[ii][isou][2]*diippf[2]);
          }
          for (int isou = 0; isou < 3; isou++) {
            cs_real_t pfacd = inc*cofafv[face_id][isou];
            for (int jsou = 0; jsou < 3; jsou++) {
              pfacd += cofbfv[face_id][isou][jsou]*pipp[jsou];
            }

            cs_real_t flux = b_visc[face_id]*pfacd;
            rhs[ii][isou] -= thetap * flux;

          } /* isou */

        }
      }
    }

    /* The vector is internal_coupled and an implicit contribution
     * is required */
    if (icoupl > 0) {

      /* Exchange pvar */
      BFT_MALLOC(pvar_local, n_local, cs_real_3_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               3, /* Dimension */
                                               (const cs_real_t*)_pvar,
                                               (cs_real_t *)pvar_local);

      /* Exchange grad */
      BFT_MALLOC(grad_local, n_local, cs_real_33_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               9, /* Dimension */
                                               (const cs_real_t*)grad,
                                               (cs_real_t *)grad_local);

      /* Exchange viscce */
      BFT_MALLOC(viscce_local, n_local, cs_real_6_t);
      cs_internal_coupling_exchange_by_cell_id(cpl,
                                               6, /* Dimension */
                                               (const cs_real_t*)viscce,
                                               (cs_real_t *)viscce_local);

      /* Exchange weighb */
      BFT_MALLOC(weighb_local, n_local, cs_real_t);
      cs_internal_coupling_exchange_by_face_id(cpl,
                                               1, /* Dimension */
                                               (const cs_real_t*)weighb,
                                               (cs_real_t *)weighb_local);

      /* Exchange diffusion limiter */
      if (df_limiter != NULL) {
        BFT_MALLOC(df_limiter_local, n_local, cs_real_t);
        cs_internal_coupling_exchange_var(cpl,
                                          1, /* Dimension */
                                          df_limiter,
                                          df_limiter_local);
      }

      /* Flux contribution */
      for (cs_lnum_t jj = 0; jj < n_local; jj++) {
        cs_lnum_t face_id = faces_local[jj];
        cs_lnum_t ii = b_face_cells[face_id];

        cs_real_t pipp[3], pjpp[3];
        cs_real_t pi[3], pj[3];

        for (int isou = 0; isou < 3; isou++) {
          pi[isou] = _pvar[ii][isou];
          pj[isou] = pvar_local[jj][isou];
        }

        cs_real_t bldfrp = (cs_real_t) ircflp;
        /* Local limitation of the reconstruction */
        if (df_limiter != NULL && ircflp > 0)
          bldfrp = CS_MAX(CS_MIN(df_limiter_local[ii], df_limiter[jj]), 0.);

        /* Recompute II" and JJ" */
        cs_real_t visci[3][3], viscj[3][3];
        cs_real_t diippf[3], djjppf[3];

        visci[0][0] = viscce[ii][0];
        visci[1][1] = viscce[ii][1];
        visci[2][2] = viscce[ii][2];
        visci[1][0] = viscce[ii][3];
        visci[0][1] = viscce[ii][3];
        visci[2][1] = viscce[ii][4];
        visci[1][2] = viscce[ii][4];
        visci[2][0] = viscce[ii][5];
        visci[0][2] = viscce[ii][5];

        /* IF.Ki.S / ||Ki.S||^2 */
        cs_real_t fikdvi = weighb[face_id];

        /* II" = IF + FI" */
        for (int i = 0; i < 3; i++) {
          diippf[i] = b_face_cog[face_id][i]-cell_cen[ii][i]
                    - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                             + visci[1][i]*b_face_normal[face_id][1]
                             + visci[2][i]*b_face_normal[face_id][2] );
        }

        viscj[0][0] = viscce_local[jj][0];
        viscj[1][1] = viscce_local[jj][1];
        viscj[2][2] = viscce_local[jj][2];
        viscj[1][0] = viscce_local[jj][3];
        viscj[0][1] = viscce_local[jj][3];
        viscj[2][1] = viscce_local[jj][4];
        viscj[1][2] = viscce_local[jj][4];
        viscj[2][0] = viscce_local[jj][5];
        viscj[0][2] = viscce_local[jj][5];

        /* FJ.Kj.S / ||Kj.S||^2
         * weighb_local defined with vector JF and surface -S */
        cs_real_t fjkdvi = weighb_local[jj];

        /* JJ" = JF + FJ"
         *   */
        for (int i = 0; i < 3; i++) {
          djjppf[i] = b_face_cog[face_id][i]-cell_cen[ii][i]-cpl->ci_cj_vect[jj][i]
                    + fjkdvi*( viscj[0][i]*b_face_normal[face_id][0]
                             + viscj[1][i]*b_face_normal[face_id][1]
                             + viscj[2][i]*b_face_normal[face_id][2] );
        }

        for (int isou = 0; isou < 3; isou++) {
          /* p in I" and J" */
          pipp[isou] = pi[isou] + bldfrp*(  grad[ii][isou][0]*diippf[0]
                                          + grad[ii][isou][1]*diippf[1]
                                          + grad[ii][isou][2]*diippf[2]);
          pjpp[isou] = pj[isou] + bldfrp*(  grad_local[jj][isou][0]*djjppf[0]
                                          + grad_local[jj][isou][1]*djjppf[1]
                                          + grad_local[jj][isou][2]*djjppf[2]);

          /* Reproduce multiplication by i_visc[face_id] */
          cs_real_t flux = (pipp[isou] - pjpp[isou])
            / (weighb[face_id] + weighb_local[jj]);

          rhs[ii][isou] -= thetap*flux;
        }

      }

      /* Remote data no longer needed */
      BFT_FREE(pvar_local);
      if (df_limiter != NULL)
        BFT_FREE(df_limiter_local);
      BFT_FREE(grad_local);
      BFT_FREE(viscce_local);
      BFT_FREE(weighb_local);

    }


  } /* idtvar */

  /* Free memory */
  BFT_FREE(grad);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the diffusion terms with a symmetric tensor
 * diffusivity for a transport equation of a scalar field \f$ \varia \f$.
 *
 * More precisely, the right hand side \f$ Rhs \f$ is updated as
 * follows:
 * \f[
 * Rhs = Rhs - \sum_{\fij \in \Facei{\celli}}      \left(
 *      - \tens{\mu}_\fij \gradv_\fij \varia \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * Warning:
 * - \f$ Rhs \f$ has already been initialized before
 *   calling cs_anisotropic_diffusion_scalar!
 * - mind the sign minus
 *
 * \param[in]     idtvar        indicator of the temporal scheme
 * \param[in]     f_id          index of the current variable
 * \param[in]     var_cal_opt   variable calculation options
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     pvara         solved variable (previous time step)
 * \param[in]     coefa         boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefb         boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofaf         boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbf         boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     viscel        symmetric cell tensor \f$ \tens{\mu}_\celli \f$
 * \param[in]     weighf        internal face weight between cells i j in case
 *                               of tensor diffusion
 * \param[in]     weighb        boundary face weight for cells i in case
 *                               of tensor diffusion
 * \param[in,out] rhs           right hand side \f$ \vect{Rhs} \f$
 */
/*----------------------------------------------------------------------------*/

void
cs_anisotropic_diffusion_tensor(int                         idtvar,
                                int                         f_id,
                                const cs_var_cal_opt_t      var_cal_opt,
                                int                         inc,
                                cs_real_6_t       *restrict pvar,
                                const cs_real_6_t *restrict pvara,
                                const cs_real_6_t           coefa[],
                                const cs_real_66_t          coefb[],
                                const cs_real_6_t           cofaf[],
                                const cs_real_66_t          cofbf[],
                                const cs_real_t             i_visc[],
                                const cs_real_t             b_visc[],
                                cs_real_6_t     *restrict   viscel,
                                const cs_real_2_t           weighf[],
                                const cs_real_t             weighb[],
                                cs_real_6_t     *restrict   rhs)
{
  const int nswrgp = var_cal_opt.nswrgr;
  const int imrgra = var_cal_opt.imrgra;
  const int imligp = var_cal_opt.imligr;
  const int ircflp = var_cal_opt.ircflu;
  const int iwarnp = var_cal_opt.verbosity;
  const double epsrgp = var_cal_opt.epsrgr;
  const double climgp = var_cal_opt.climgr;
  const double relaxp = var_cal_opt.relaxv;
  const double thetap = var_cal_opt.thetav;

  const cs_mesh_t  *m = cs_glob_mesh;
  const cs_halo_t  *halo = m->halo;
  cs_mesh_quantities_t  *fvq = cs_glob_mesh_quantities;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];

  cs_real_6_t *viscce;
  cs_real_6_t *w2;
  cs_real_63_t *grad;

  cs_field_t *f;

  /* 1. Initialization */

  viscce = NULL;
  w2 = NULL;

  /* Allocate work arrays */
  BFT_MALLOC(grad, n_cells_ext, cs_real_63_t);

  /* Choose gradient type */
  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  /* Handle cases where only the previous values (already synchronized)
     or current values are provided */

  if (pvar != NULL && m->halo != NULL) {
    cs_halo_sync_var_strided(m->halo, halo_type, (cs_real_t *)pvar, 6);
    if (cs_glob_mesh->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(m->halo, halo_type, (cs_real_t *)pvar);
  }
  else if (pvara == NULL)
    pvara = (const cs_real_6_t *restrict)pvar;

  const cs_real_6_t  *restrict _pvar
    = (pvar != NULL) ? (const cs_real_6_t  *restrict)pvar : pvara;

  /* Logging info */

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id
      = cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[anisotropic diffusion, tensor]", 63);
  var_name[63] = '\0';

  /* Porosity fields */
  cs_field_t *fporo = cs_field_by_name_try("porosity");
  cs_field_t *ftporo = cs_field_by_name_try("tensorial_porosity");

  cs_real_t *porosi = NULL;
  cs_real_6_t *porosf = NULL;

  if (cs_glob_porous_model == 1 || cs_glob_porous_model == 2) {
    porosi = fporo->val;
    if (ftporo != NULL) {
      porosf = (cs_real_6_t *)ftporo->val;
    }
  }

  /* Without porosity */
  if (porosi == NULL) {
    viscce = viscel;

    /* With porosity */
  } else if (porosi != NULL && porosf == NULL) {
    BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
    for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
      for (int isou = 0; isou < 6; isou++) {
        w2[cell_id][isou] = porosi[cell_id]*viscel[cell_id][isou];
      }
    }
    viscce = w2;

    /* With tensorial porosity */
  } else if (porosi != NULL && porosf != NULL) {
    BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
    for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
      cs_math_sym_33_product(porosf[cell_id],
                             viscel[cell_id],
                             w2[cell_id]);
    }
    viscce = w2;
  }

  /* ---> Periodicity and parallelism treatment of symmetric tensors */
  if (halo != NULL) {
    cs_halo_sync_var_strided(halo, halo_type, (cs_real_t *)viscce, 6);
    if (m->n_init_perio > 0)
      cs_halo_perio_sync_var_sym_tens(halo, halo_type, (cs_real_t *)viscce);
  }

  /* 2. Compute the diffusive part with reconstruction technics */

  /* ======================================================================
     ---> Compute the gradient of the current variable if needed
     ======================================================================*/

  if (ircflp == 1) {

    cs_gradient_tensor_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    nswrgp,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    coefa,
                                    coefb,
                                    _pvar,
                                    grad);

  } else {
#   pragma omp parallel for
    for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 6; isou++) {
        for (int jsou = 0; jsou < 3; jsou++)
          grad[cell_id][isou][jsou] = 0.;
      }
    }
  }

  /* ======================================================================
     ---> Contribution from interior faces
     ======================================================================*/

  if (n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext -n_cells > CS_THR_MIN)
    for (cs_lnum_t cell_id = n_cells; cell_id < n_cells_ext; cell_id++) {
      for (int isou = 0; isou < 6; isou++) {
        rhs[cell_id][isou] = 0.;
      }
    }
  }

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t visci[3][3], viscj[3][3];
          cs_real_t diippf[3], djjppf[3], pipp[6], pjpp[6];
          cs_real_t  pir[6], pjr[6], pippr[6], pjppr[6];
          cs_real_t  pi[6], pj[6], pia[6], pja[6];

          for (int isou = 0; isou < 6; isou++) {
            pi[isou] = _pvar[ii][isou];
            pj[isou] = _pvar[jj][isou];
            pia[isou] = pvara[ii][isou];
            pja[isou] = pvara[jj][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);


          /* Recompute II" and JJ"
             ----------------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          for (int isou = 0; isou < 6; isou++) {
            /* p in I" and J" */
            pipp[isou] = pi[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                           + grad[ii][isou][1]*diippf[1]
                                           + grad[ii][isou][2]*diippf[2]);
            pjpp[isou] = pj[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                           + grad[jj][isou][1]*djjppf[1]
                                           + grad[jj][isou][2]*djjppf[2]);

            pir[isou] = pi[isou]/relaxp - (1.-relaxp)/relaxp * pia[isou];
            pjr[isou] = pj[isou]/relaxp - (1.-relaxp)/relaxp * pja[isou];


            /* pr in I" and J" */
            pippr[isou] = pir[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                             + grad[ii][isou][1]*diippf[1]
                                             + grad[ii][isou][2]*diippf[2]);
            pjppr[isou] = pjr[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                             + grad[jj][isou][1]*djjppf[1]
                                             + grad[jj][isou][2]*djjppf[2]);


            cs_real_t fluxi = i_visc[face_id]*(pippr[isou] - pjpp[isou]);
            cs_real_t fluxj = i_visc[face_id]*(pipp[isou] - pjppr[isou]);

            rhs[ii][isou] -= fluxi;
            rhs[jj][isou] += fluxj;
          } // loop on isou
        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          cs_real_t visci[3][3], viscj[3][3];
          cs_real_t diippf[3], djjppf[3], pipp[6], pjpp[6];
          cs_real_t pi[6], pj[6];

          for (int isou = 0; isou < 6; isou++) {
            pi[isou] = _pvar[ii][isou];
            pj[isou] = _pvar[jj][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);

          /* Recompute II" and JJ"
             ----------------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          cs_real_t fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          for (int isou = 0; isou < 6; isou++) {
            /* p in I" and J" */
            pipp[isou] = pi[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                           + grad[ii][isou][1]*diippf[1]
                                           + grad[ii][isou][2]*diippf[2]);
            pjpp[isou] = pj[isou] + bldfrp*( grad[jj][isou][0]*djjppf[0]
                                           + grad[jj][isou][1]*djjppf[1]
                                           + grad[jj][isou][2]*djjppf[2]);

            cs_real_t flux = i_visc[face_id]*(pipp[isou] -pjpp[isou]);

            rhs[ii][isou] -= thetap*flux;
            rhs[jj][isou] += thetap*flux;
          }
        }
      }
    }
  }

  /* ======================================================================
     ---> Contribution from boundary faces
     ======================================================================*/

  /* Steady */
  if (idtvar < 0) {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t pi[6], pia[6], pir[6], pippr[6];
          cs_real_t visci[3][3];
          cs_real_t diippf[3];

          for (int isou = 0; isou < 6; isou++) {
            pi[isou] = _pvar[ii][isou];
            pia[isou] = pvara[ii][isou];
            pir[isou] = pi[isou]/relaxp - (1.-relaxp)/relaxp*pia[isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2] );
          }
          for (int isou = 0; isou < 6; isou++) {
            pippr[isou] = pir[isou] + bldfrp*( grad[ii][isou][0]*diippf[0]
                                             + grad[ii][isou][1]*diippf[1]
                                             + grad[ii][isou][2]*diippf[2]);
          }
          for (int isou = 0; isou < 6; isou++) {
            cs_real_t pfacd = inc*cofaf[face_id][isou];
            for (int jsou = 0; jsou < 6; jsou++) {
              pfacd += cofbf[face_id][isou][jsou]*pippr[jsou];
            }

            cs_real_t flux = b_visc[face_id]*pfacd;
            rhs[ii][isou] -= flux;
          }
        }
      }
    }

    /* Unsteady */
  } else {

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          cs_real_t visci[3][3];
          cs_real_t diippf[3], pi[6], pipp[6];

          for (int isou = 0; isou < 6; isou++) {
            pi[isou] = _pvar[ii][isou];
          }

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);


          /* Recompute II"
             --------------*/

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2]);
          }
          for (int isou = 0; isou < 6; isou++) {
            pipp[isou] = pi[isou] + bldfrp * ( grad[ii][isou][0]*diippf[0]
                                               + grad[ii][isou][1]*diippf[1]
                                               + grad[ii][isou][2]*diippf[2]);
          }
          for (int isou = 0; isou < 6; isou++) {
            cs_real_t pfacd = inc*cofaf[face_id][isou];
            for (int jsou = 0; jsou < 6; jsou++) {
              pfacd += cofbf[face_id][isou][jsou]*pipp[jsou];
            }

            cs_real_t flux = b_visc[face_id]*pfacd;
            rhs[ii][isou] -= thetap*flux;
          }

        }
      }
    }

  }

  /* Free memory */
  BFT_FREE(grad);
  BFT_FREE(w2);
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Update the face mass flux with the face pressure (or pressure
 * increment, or pressure double increment) gradient.
 *
 * <a name="itrmas"></a>
 *
 * \f[
 * \dot{m}_\ij = \dot{m}_\ij
 *             - \Delta t \grad_\fij \delta p \cdot \vect{S}_\ij
 * \f]
 *
 * Please refer to the
 * <a href="../../theory.pdf#itrmas"><b>itrmas/itrgrp</b></a> section of the
 * theory guide for more information.
 *
 * \param[in]     f_id          field id (or -1)
 * \param[in]     m             pointer to mesh
 * \param[in]     fvq           pointer to finite volume quantities
 * \param[in]     init          indicator
 *                               - 1 initialize the mass flux to 0
 *                               - 0 otherwise
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     imrgra        indicator
 *                               - 0 iterative gradient
 *                               - 1 least squares gradient
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
 *                                 (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     nswrgp        number of reconstruction sweeps for the
 *                               gradients
 * \param[in]     imligp        clipping gradient method
 *                               - < 0 no clipping
 *                               - = 0 thank to neighbooring gradients
 *                               - = 1 thank to the mean gradient
 * \param[in]     iphydp        hydrostatic pressure indicator
 * \param[in]     iwgrp         indicator
 *                               - 1 weight gradient by vicosity*porosity
 *                               - weighting determined by field options
 * \param[in]     iwarnp        verbosity
 * \param[in]     epsrgp        relative precision for the gradient
 *                               reconstruction
 * \param[in]     climgp        clipping coeffecient for the computation of
 *                               the gradient
 * \param[in]     frcxt         body force creating the hydrostatic pressure
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     visel         viscosity by cell
 * \param[in,out] i_massflux    mass flux at interior faces
 * \param[in,out] b_massflux    mass flux at boundary faces
 */
/*----------------------------------------------------------------------------*/

void
cs_face_diffusion_potential(const int                 f_id,
                            const cs_mesh_t          *m,
                            cs_mesh_quantities_t     *fvq,
                            int                       init,
                            int                       inc,
                            int                       imrgra,
                            int                       iccocg,
                            int                       nswrgp,
                            int                       imligp,
                            int                       iphydp,
                            int                       iwgrp,
                            int                       iwarnp,
                            double                    epsrgp,
                            double                    climgp,
                            cs_real_3_t     *restrict frcxt,
                            cs_real_t       *restrict pvar,
                            const cs_real_t           coefap[],
                            const cs_real_t           coefbp[],
                            const cs_real_t           cofafp[],
                            const cs_real_t           cofbfp[],
                            const cs_real_t           i_visc[],
                            const cs_real_t           b_visc[],
                            cs_real_t       *restrict visel,
                            cs_real_t       *restrict i_massflux,
                            cs_real_t       *restrict b_massflux)
{
  const cs_halo_t  *halo = m->halo;

  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;
  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_f_face_surf = fvq->i_f_face_surf;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  /* Local variables */

  char var_name[64];
  int tr_dim = 0;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_3_t *grad;
  cs_field_t *f;

  cs_real_t *gweight = NULL;

  /*==========================================================================*/

  /* i_visc and carry similar information */

  /*============================================================================
    1. Initialization
    ==========================================================================*/

  if (init >= 1) {
#   pragma omp parallel for
    for (cs_lnum_t face_id = 0; face_id < m->n_i_faces; face_id++) {
      i_massflux[face_id] = 0.;
    }
#   pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
    for (cs_lnum_t face_id = 0; face_id < m->n_b_faces; face_id++) {
      b_massflux[face_id] = 0.;
    }
  } else if (init != 0) {
    bft_error(__FILE__, __LINE__, 0,
              _("invalid value of init"));
  }

  /* Use iterative gradient */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  if (imrgra < 0)
    imrgra = 0;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  if (f_id > -1) {
    f = cs_field_by_id(f_id);
    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[face mass flux update]", 63);
  var_name[63] = '\0';

  /* Handle parallelism and periodicity */

  if (halo != NULL)
    cs_halo_sync_var(halo, halo_type, pvar);

  /*==========================================================================
    2. Update mass flux without reconstruction technics
    ==========================================================================*/

  if (nswrgp <= 1) {

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          i_massflux[face_id] += i_visc[face_id]*(pvar[ii] - pvar[jj]);

        }
      }
    }

    /* Mass flow through boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];
          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pvar[ii];

          b_massflux[face_id] += b_visc[face_id]*pfac;

        }
      }
    }

  }

  /*==========================================================================
    3. Update mass flux with reconstruction technique if the mesh is non
       orthogonal
    ==========================================================================*/

  if (nswrgp > 1) {

    /* Allocate a work array for the gradient calculation */
    BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

    /* Compute gradient */
    if (iwgrp > 0) {
      gweight = visel;
      if (halo != NULL)
        cs_halo_sync_var(halo, halo_type, gweight);
    }

    else if (f_id > -1) {
      /* Get the calculation option from the field */
      int key_cal_opt_id = cs_field_key_id("var_cal_opt");
      cs_var_cal_opt_t var_cal_opt;
      cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    iphydp,
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    frcxt,
                                    coefap,
                                    coefbp,
                                    (const cs_real_t *)pvar,
                                    gweight, /* Weighted gradient */
                                    NULL, /* internal coupling */
                                    grad);

    /* Handle parallelism and periodicity */

    if (halo != NULL)
      cs_halo_sync_var(halo, halo_type, visel);

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double dpxf = 0.5*(  visel[ii]*grad[ii][0]
                             + visel[jj]*grad[jj][0]);
          double dpyf = 0.5*(  visel[ii]*grad[ii][1]
                             + visel[jj]*grad[jj][1]);
          double dpzf = 0.5*(  visel[ii]*grad[ii][2]
                             + visel[jj]*grad[jj][2]);

          /*---> Dij = IJ - (IJ.N) N = II' - JJ' */
          double dijx = diipf[face_id][0] - djjpf[face_id][0];
          double dijy = diipf[face_id][1] - djjpf[face_id][1];
          double dijz = diipf[face_id][2] - djjpf[face_id][2];

          i_massflux[face_id] =  i_massflux[face_id]
                               + i_visc[face_id]*(pvar[ii] - pvar[jj])
                               +  (dpxf *dijx + dpyf*dijy + dpzf*dijz)
                                 * i_f_face_surf[face_id]/i_dist[face_id];

        }
      }
    }

    /* Mass flow through boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          double diipbx = diipb[face_id][0];
          double diipby = diipb[face_id][1];
          double diipbz = diipb[face_id][2];

          double pip = pvar[ii] + grad[ii][0]*diipbx
                                 + grad[ii][1]*diipby
                                 + grad[ii][2]*diipbz;
          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pip;

          b_massflux[face_id] += b_visc[face_id]*pfac;

        }
      }
    }

    /* Free memory */
    BFT_FREE(grad);
  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the pressure gradient term to the mass flux
 * in case of anisotropic diffusion of the pressure field \f$ P \f$.
 *
 * More precisely, the mass flux side \f$ \dot{m}_\fij \f$ is updated as
 * follows:
 * \f[
 * \dot{m}_\fij = \dot{m}_\fij -
 *              \left( \tens{\mu}_\fij \gradv_\fij P \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * \param[in]     f_id          field id (or -1)
 * \param[in]     m             pointer to mesh
 * \param[in]     fvq           pointer to finite volume quantities
 * \param[in]     init           indicator
 *                               - 1 initialize the mass flux to 0
 *                               - 0 otherwise
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     imrgra        indicator
 *                               - 0 iterative gradient
 *                               - 1 least squares gradient
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
                                    (for iterativ gradients)
 *                               - 0 otherwise
 * \param[in]     nswrgp        number of reconstruction sweeps for the
 *                               gradients
 * \param[in]     imligp        clipping gradient method
 *                               - < 0 no clipping
 *                               - = 0 thank to neighbooring gradients
 *                               - = 1 thank to the mean gradient
 * \param[in]     ircflp        indicator
 *                               - 1 flux reconstruction,
 *                               - 0 otherwise
 * \param[in]     iphydp        indicator
 *                               - 1 hydrostatic pressure taken into account
 *                               - 0 otherwise
 * \param[in]     iwgrp         indicator
 *                               - 1 weight gradient by vicosity*porosity
 *                               - weighting determined by field options
 * \param[in]     iwarnp        verbosity
 * \param[in]     epsrgp        relative precision for the gradient
 *                               reconstruction
 * \param[in]     climgp        clipping coeffecient for the computation of
 *                               the gradient
 * \param[in]     frcxt         body force creating the hydrostatic pressure
 * \param[in]     pvar          solved variable (pressure)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     viscel        symmetric cell tensor \f$ \tens{\mu}_\celli \f$
 * \param[in]     weighf        internal face weight between cells i j in case
 *                               of tensor diffusion
 * \param[in]     weighb        boundary face weight for cells i in case
 *                               of tensor diffusion
 * \param[in,out] i_massflux    mass flux at interior faces
 * \param[in,out] b_massflux    mass flux at boundary faces
 */
/*----------------------------------------------------------------------------*/

void
cs_face_anisotropic_diffusion_potential(const int                 f_id,
                                        const cs_mesh_t          *m,
                                        cs_mesh_quantities_t     *fvq,
                                        int                       init,
                                        int                       inc,
                                        int                       imrgra,
                                        int                       iccocg,
                                        int                       nswrgp,
                                        int                       imligp,
                                        int                       ircflp,
                                        int                       iphydp,
                                        int                       iwgrp,
                                        int                       iwarnp,
                                        double                    epsrgp,
                                        double                    climgp,
                                        cs_real_3_t     *restrict frcxt,
                                        cs_real_t       *restrict pvar,
                                        const cs_real_t           coefap[],
                                        const cs_real_t           coefbp[],
                                        const cs_real_t           cofafp[],
                                        const cs_real_t           cofbfp[],
                                        const cs_real_t           i_visc[],
                                        const cs_real_t           b_visc[],
                                        cs_real_6_t     *restrict viscel,
                                        const cs_real_2_t         weighf[],
                                        const cs_real_t           weighb[],
                                        cs_real_t       *restrict i_massflux,
                                        cs_real_t       *restrict b_massflux)
{
  const cs_halo_t  *halo = m->halo;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;

  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];
  int tr_dim = 0;
  int w_stride = 6;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_6_t *viscce;
  cs_real_6_t *w2;
  cs_real_3_t *grad;
  cs_field_t *f = NULL;

  cs_real_t *gweight = NULL;

  /*==========================================================================
    1. Initialization
    ==========================================================================*/

  if (init >= 1) {
    #pragma omp parallel for
    for (cs_lnum_t face_id = 0; face_id < m->n_i_faces; face_id++) {
      i_massflux[face_id] = 0.;
    }
    for (cs_lnum_t face_id = 0; face_id < m->n_b_faces; face_id++) {
      b_massflux[face_id] = 0.;
    }
  } else if (init != 0) {
      bft_error(__FILE__, __LINE__, 0,
                _("invalid value of init"));
  }

  /* Use iterative gradient */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  if (imrgra < 0)
    imrgra = 0;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  if (f_id > -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id =
      cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;

    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[face mass flux update]", 63);
  var_name[63] = '\0';

  /* Porosity fields */
  cs_field_t *fporo = cs_field_by_name_try("porosity");
  cs_field_t *ftporo = cs_field_by_name_try("tensorial_porosity");

  cs_real_t *porosi = NULL;
  cs_real_6_t *porosf = NULL;

  if (cs_glob_porous_model == 1 || cs_glob_porous_model == 2) {
    porosi = fporo->val;
    if (ftporo != NULL) {
      porosf = (cs_real_6_t *)ftporo->val;
    }
  }

  /* Handle parallelism and periodicity */

  if (halo != NULL)
    cs_halo_sync_var(halo, halo_type, pvar);

  /*==========================================================================
    2. Update mass flux without reconstruction technique
    ==========================================================================*/

  if (nswrgp <= 1) {

    /* ---> Contribution from interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          i_massflux[face_id] += i_visc[face_id]*(pvar[ii] - pvar[jj]);

        }
      }
    }

    /* ---> Contribution from boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];
          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pvar[ii];

          b_massflux[face_id] += b_visc[face_id]*pfac;

        }
      }
    }

  }

  /*==========================================================================
    3. Update mass flux with reconstruction technique
    ==========================================================================*/

  if (nswrgp > 1) {

    viscce = NULL;
    w2 = NULL;

    /* Without porosity */
    if (porosi == NULL) {
      viscce = viscel;

      /* With porosity */
    } else if (porosi != NULL && porosf == NULL) {
      BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
      for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
        for (int isou = 0; isou < 6; isou++) {
          w2[cell_id][isou] = porosi[cell_id]*viscel[cell_id][isou];
        }
      }
      viscce = w2;

      /* With tensorial porosity */
    } else if (porosi != NULL && porosf != NULL) {
      BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
      for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
        cs_math_sym_33_product(porosf[cell_id],
                               viscel[cell_id],
                               w2[cell_id]);
      }
      viscce = w2;
    }

    /* ---> Periodicity and parallelism treatment of symmetric tensors */

    if (halo != NULL) {
      cs_halo_sync_var_strided(halo, CS_HALO_STANDARD, (cs_real_t *)viscce, 6);

      if (m->n_init_perio > 0)
        cs_halo_perio_sync_var_sym_tens(halo,
                                        CS_HALO_STANDARD,
                                        (cs_real_t *)viscce);
    }

    /* Allocate a work array for the gradient calculation */
    BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

    /* Compute gradient */
    if (iwgrp > 0) {
      gweight = (cs_real_t *)viscce;
      if (halo != NULL) {
        cs_halo_sync_var_strided(halo, halo_type, gweight, 6);
        if (cs_glob_mesh->n_init_perio > 0)
          cs_halo_perio_sync_var_sym_tens(halo, halo_type, gweight);
      }
    }

    else if (f_id > -1) {
      /* Get the calculation option from the field */
      int key_cal_opt_id = cs_field_key_id("var_cal_opt");
      cs_var_cal_opt_t var_cal_opt;
      cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idifft > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    /* Compute gradient */
    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    iphydp,
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    frcxt,
                                    coefap,
                                    coefbp,
                                    pvar,
                                    gweight, /* Weighted gradient */
                                    NULL, /* internal coupling */
                                    grad);

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double pi = pvar[ii];
          double pj = pvar[jj];

          /* Recompute II" and JJ"
             ----------------------*/

          cs_real_t visci[3][3], viscj[3][3];
          cs_real_t diippf[3], djjppf[3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);


          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*(  visci[0][i]*i_face_normal[face_id][0]
                                + visci[1][i]*i_face_normal[face_id][1]
                                + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          double fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*(  viscj[0][i]*i_face_normal[face_id][0]
                                + viscj[1][i]*i_face_normal[face_id][1]
                                + viscj[2][i]*i_face_normal[face_id][2] );
          }

          /* p in I" and J" */
          double pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                     + grad[ii][1]*diippf[1]
                                     + grad[ii][2]*diippf[2]);
          double pjpp = pj + bldfrp*(  grad[jj][0]*djjppf[0]
                                     + grad[jj][1]*djjppf[1]
                                     + grad[jj][2]*djjppf[2]);

          i_massflux[face_id] += i_visc[face_id]*(pipp - pjpp);

        }
      }
    }

    /* ---> Contribution from boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          double pi = pvar[ii];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          cs_real_t visci[3][3];
          cs_real_t diippf[3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighb[face_id];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*(  visci[0][i]*b_face_normal[face_id][0]
                                + visci[1][i]*b_face_normal[face_id][1]
                                + visci[2][i]*b_face_normal[face_id][2] );
          }

          double pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                     + grad[ii][1]*diippf[1]
                                     + grad[ii][2]*diippf[2]);


          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pipp;

          b_massflux[face_id] += b_visc[face_id]*pfac;

        }
      }
    }

    /* Free memory */
    BFT_FREE(grad);
    BFT_FREE(w2);

  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Update the cell mass flux divergence with the face pressure (or
 * pressure increment, or pressure double increment) gradient.
 *
 * \f[
 * \dot{m}_\ij = \dot{m}_\ij
 *             - \sum_j \Delta t \grad_\fij p \cdot \vect{S}_\ij
 * \f]
 *
 * \param[in]     f_id          field id (or -1)
 * \param[in]     m             pointer to mesh
 * \param[in]     fvq           pointer to finite volume quantities
 * \param[in]     init          indicator
 *                               - 1 initialize the mass flux to 0
 *                               - 0 otherwise
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     imrgra        indicator
 *                               - 0 iterative gradient
 *                               - 1 least squares gradient
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
 *                                 (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     nswrgp        number of reconstruction sweeps for the
 *                               gradients
 * \param[in]     imligp        clipping gradient method
 *                               - < 0 no clipping
 *                               - = 0 thank to neighbooring gradients
 *                               - = 1 thank to the mean gradient
 * \param[in]     iphydp        hydrostatic pressure indicator
 * \param[in]     iwarnp        verbosity
 * \param[in]     iwgrp         indicator
 *                               - 1 weight gradient by vicosity*porosity
 *                               - weighting determined by field options
 * \param[in]     epsrgp        relative precision for the gradient
 *                               reconstruction
 * \param[in]     climgp        clipping coeffecient for the computation of
 *                               the gradient
 * \param[in]     frcxt         body force creating the hydrostatic pressure
 * \param[in]     pvar          solved variable (current time step)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     visel         viscosity by cell
 * \param[in,out] diverg        mass flux divergence
 */
/*----------------------------------------------------------------------------*/

void
cs_diffusion_potential(const int                 f_id,
                       const cs_mesh_t          *m,
                       cs_mesh_quantities_t     *fvq,
                       int                       init,
                       int                       inc,
                       int                       imrgra,
                       int                       iccocg,
                       int                       nswrgp,
                       int                       imligp,
                       int                       iphydp,
                       int                       iwgrp,
                       int                       iwarnp,
                       double                    epsrgp,
                       double                    climgp,
                       cs_real_3_t     *restrict frcxt,
                       cs_real_t       *restrict pvar,
                       const cs_real_t           coefap[],
                       const cs_real_t           coefbp[],
                       const cs_real_t           cofafp[],
                       const cs_real_t           cofbfp[],
                       const cs_real_t           i_visc[],
                       const cs_real_t           b_visc[],
                       cs_real_t                 visel[],
                       cs_real_t       *restrict diverg)
{
  const cs_halo_t  *halo = m->halo;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_t *restrict i_dist = fvq->i_dist;
  const cs_real_t *restrict i_f_face_surf = fvq->i_f_face_surf;
  const cs_real_3_t *restrict diipf
    = (const cs_real_3_t *restrict)fvq->diipf;
  const cs_real_3_t *restrict djjpf
    = (const cs_real_3_t *restrict)fvq->djjpf;
  const cs_real_3_t *restrict diipb
    = (const cs_real_3_t *restrict)fvq->diipb;

  /* Local variables */

  char var_name[64];
  int tr_dim = 0;
  int mass_flux_rec_type = cs_glob_stokes_model->irecmf;
  int w_stride = 1;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_3_t *grad;
  cs_field_t *f;

  cs_real_t *gweight = NULL;

  /*==========================================================================*/

  /*==========================================================================
    1. Initialization
    ==========================================================================*/

  if (init >= 1) {
#   pragma omp parallel for
    for (cs_lnum_t ii = 0; ii < n_cells_ext; ii++) {
      diverg[ii] = 0.;
    }
  } else if (init == 0 && n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext - n_cells > CS_THR_MIN)
    for (cs_lnum_t ii = n_cells; ii < n_cells_ext; ii++) {
      diverg[ii] = 0.;
    }
  } else if (init != 0) {
    bft_error(__FILE__, __LINE__, 0,
              _("invalid value of init"));
  }

  /* Use iterative gradient */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  if (imrgra < 0)
    imrgra = 0;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);
  if (f_id != -1) {
    f = cs_field_by_id(f_id);
    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[cell mass flux divergence update]", 63);
  var_name[63] = '\0';

  /* Handle parallelism and periodicity */

  if (halo != NULL)
    cs_halo_sync_var(halo, halo_type, pvar);

  /*==========================================================================
    2. Update mass flux without reconstruction technics
    ==========================================================================*/

  if (nswrgp <= 1) {

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double i_massflux = i_visc[face_id]*(pvar[ii] - pvar[jj]);
          diverg[ii] += i_massflux;
          diverg[jj] -= i_massflux;

        }
      }
    }

    /* Mass flow through boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];
          double pfac = inc*cofafp[face_id] +cofbfp[face_id]*pvar[ii];

          double b_massflux = b_visc[face_id]*pfac;
          diverg[ii] += b_massflux;

        }
      }
    }

  }

  /*==========================================================================
    3. Update mass flux with reconstruction technics if the mesh is non
       orthogonal
    ==========================================================================*/

  if (nswrgp > 1) {

    /* Allocate a work array for the gradient calculation */
    BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

    /* Compute gradient */
    if (iwgrp > 0) {
      gweight = visel;
      if (halo != NULL)
        cs_halo_sync_var(halo, halo_type, gweight);
    }

    else if (f_id > -1) {
      /* Get the calculation option from the field */
      int key_cal_opt_id = cs_field_key_id("var_cal_opt");
      cs_var_cal_opt_t var_cal_opt;
      cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idiff > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    cs_real_t *_pvar = NULL;

    if (cs_glob_mesh_quantities_flag & CS_BAD_CELLS_REGULARISATION) {
      BFT_MALLOC(_pvar, n_cells_ext, cs_real_t);

      for (cs_lnum_t cell_id = 0; cell_id < n_cells_ext; cell_id++)
        _pvar[cell_id] = pvar[cell_id];

      cs_bad_cells_regularisation_scalar(_pvar);
    } else {
      _pvar = pvar;
    }

    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    iphydp,
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    frcxt,
                                    coefap,
                                    coefbp,
                                    _pvar,
                                    gweight, /* Weighted gradient */
                                    NULL, /* internal coupling */
                                    grad);

    if (cs_glob_mesh_quantities_flag & CS_BAD_CELLS_REGULARISATION)
      BFT_FREE(_pvar);

    /* Handle parallelism and periodicity */

    if (halo != NULL)
      cs_halo_sync_var(halo, halo_type, visel);

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double i_massflux = i_visc[face_id]*(pvar[ii] - pvar[jj]);

          if (mass_flux_rec_type == 0) {

            /*---> Dij = IJ - (IJ.N) N = II' - JJ' */
            double dijx = diipf[face_id][0] - djjpf[face_id][0];
            double dijy = diipf[face_id][1] - djjpf[face_id][1];
            double dijz = diipf[face_id][2] - djjpf[face_id][2];

            double dpxf = 0.5*(  visel[ii]*grad[ii][0]
                               + visel[jj]*grad[jj][0]);
            double dpyf = 0.5*(  visel[ii]*grad[ii][1]
                               + visel[jj]*grad[jj][1]);
            double dpzf = 0.5*(  visel[ii]*grad[ii][2]
                               + visel[jj]*grad[jj][2]);

            i_massflux += (dpxf*dijx + dpyf*dijy + dpzf*dijz)
                          *i_f_face_surf[face_id]/i_dist[face_id];
          }
          else {
            i_massflux += i_visc[face_id]*
                          ( cs_math_3_dot_product(grad[ii], diipf[face_id])
                          - cs_math_3_dot_product(grad[jj], djjpf[face_id]));
          }

          diverg[ii] += i_massflux;
          diverg[jj] -= i_massflux;

        }
      }
    }

    /* Mass flow through boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          double diipbx = diipb[face_id][0];
          double diipby = diipb[face_id][1];
          double diipbz = diipb[face_id][2];

          double pip = pvar[ii] + grad[ii][0]*diipbx
                                + grad[ii][1]*diipby
                                + grad[ii][2]*diipbz;
          double pfac = inc*cofafp[face_id] +cofbfp[face_id]*pip;

          double b_massflux = b_visc[face_id]*pfac;
          diverg[ii] += b_massflux;

        }
      }
    }

    /* Free memory */
    BFT_FREE(grad);
  }
}

/*----------------------------------------------------------------------------*/
/*!
 * \brief Add the explicit part of the divergence of the mass flux due to the
 * pressure gradient (routine analog to diften).
 *
 * More precisely, the divergence of the mass flux side
 * \f$ \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij \f$ is updated as follows:
 * \f[
 * \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij
 *  = \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij
 *  - \sum_{\fij \in \Facei{\celli}}
 *    \left( \tens{\mu}_\fij \gradv_\fij P \cdot \vect{S}_\ij  \right)
 * \f]
 *
 * \param[in]     f_id          field id (or -1)
 * \param[in]     m             pointer to mesh
 * \param[in]     fvq           pointer to finite volume quantities
 * \param[in]     init           indicator
 *                               - 1 initialize the mass flux to 0
 *                               - 0 otherwise
 * \param[in]     inc           indicator
 *                               - 0 when solving an increment
 *                               - 1 otherwise
 * \param[in]     imrgra        indicator
 *                               - 0 iterative gradient
 *                               - 1 least squares gradient
 * \param[in]     iccocg        indicator
 *                               - 1 re-compute cocg matrix
                                     (for iterative gradients)
 *                               - 0 otherwise
 * \param[in]     nswrgp        number of reconstruction sweeps for the
 *                               gradients
 * \param[in]     imligp        clipping gradient method
 *                               - < 0 no clipping
 *                               - = 0 thank to neighbooring gradients
 *                               - = 1 thank to the mean gradient
 * \param[in]     ircflp        indicator
 *                               - 1 flux reconstruction,
 *                               - 0 otherwise
 * \param[in]     iphydp        indicator
 *                               - 1 hydrostatic pressure taken into account
 *                               - 0 otherwise
 * \param[in]     iwgrp         indicator
 *                               - 1 weight gradient by vicosity*porosity
 *                               - weighting determined by field options
 * \param[in]     iwarnp        verbosity
 * \param[in]     epsrgp        relative precision for the gradient
 *                               reconstruction
 * \param[in]     climgp        clipping coeffecient for the computation of
 *                               the gradient
 * \param[in]     frcxt         body force creating the hydrostatic pressure
 * \param[in]     pvar          solved variable (pressure)
 * \param[in]     coefap        boundary condition array for the variable
 *                               (explicit part)
 * \param[in]     coefbp        boundary condition array for the variable
 *                               (implicit part)
 * \param[in]     cofafp        boundary condition array for the diffusion
 *                               of the variable (explicit part)
 * \param[in]     cofbfp        boundary condition array for the diffusion
 *                               of the variable (implicit part)
 * \param[in]     i_visc        \f$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} \f$
 *                               at interior faces for the r.h.s.
 * \param[in]     b_visc        \f$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} \f$
 *                               at border faces for the r.h.s.
 * \param[in]     viscel        symmetric cell tensor \f$ \tens{\mu}_\celli \f$
 * \param[in]     weighf        internal face weight between cells i j in case
 *                               of tensor diffusion
 * \param[in]     weighb        boundary face weight for cells i in case
 *                               of tensor diffusion
 * \param[in,out] diverg        divergence of the mass flux
 */
/*----------------------------------------------------------------------------*/

void
cs_anisotropic_diffusion_potential(const int                 f_id,
                                   const cs_mesh_t          *m,
                                   cs_mesh_quantities_t     *fvq,
                                   int                       init,
                                   int                       inc,
                                   int                       imrgra,
                                   int                       iccocg,
                                   int                       nswrgp,
                                   int                       imligp,
                                   int                       ircflp,
                                   int                       iphydp,
                                   int                       iwgrp,
                                   int                       iwarnp,
                                   double                    epsrgp,
                                   double                    climgp,
                                   cs_real_3_t     *restrict frcxt,
                                   cs_real_t       *restrict pvar,
                                   const cs_real_t           coefap[],
                                   const cs_real_t           coefbp[],
                                   const cs_real_t           cofafp[],
                                   const cs_real_t           cofbfp[],
                                   const cs_real_t           i_visc[],
                                   const cs_real_t           b_visc[],
                                   cs_real_6_t     *restrict viscel,
                                   const cs_real_2_t         weighf[],
                                   const cs_real_t           weighb[],
                                   cs_real_t       *restrict diverg)
{
  const cs_halo_t  *halo = m->halo;

  const cs_lnum_t n_cells = m->n_cells;
  const cs_lnum_t n_cells_ext = m->n_cells_with_ghosts;
  const int n_i_groups = m->i_face_numbering->n_groups;
  const int n_i_threads = m->i_face_numbering->n_threads;
  const int n_b_groups = m->b_face_numbering->n_groups;
  const int n_b_threads = m->b_face_numbering->n_threads;
  const cs_lnum_t *restrict i_group_index = m->i_face_numbering->group_index;
  const cs_lnum_t *restrict b_group_index = m->b_face_numbering->group_index;

  const cs_lnum_2_t *restrict i_face_cells
    = (const cs_lnum_2_t *restrict)m->i_face_cells;
  const cs_lnum_t *restrict b_face_cells
    = (const cs_lnum_t *restrict)m->b_face_cells;
  const cs_real_3_t *restrict cell_cen
    = (const cs_real_3_t *restrict)fvq->cell_cen;
  const cs_real_3_t *restrict i_face_normal
    = (const cs_real_3_t *restrict)fvq->i_face_normal;
  const cs_real_3_t *restrict b_face_normal
    = (const cs_real_3_t *restrict)fvq->b_face_normal;
  const cs_real_3_t *restrict i_face_cog
    = (const cs_real_3_t *restrict)fvq->i_face_cog;
  const cs_real_3_t *restrict b_face_cog
    = (const cs_real_3_t *restrict)fvq->b_face_cog;

  /* Local variables */

  cs_real_t *df_limiter = NULL;

  char var_name[64];
  int tr_dim = 0;
  int w_stride = 6;

  bool recompute_cocg = (iccocg) ? true : false;

  cs_real_6_t *viscce = NULL;
  cs_real_6_t *w2 = NULL;
  cs_real_3_t *grad = NULL;
  cs_field_t *f = NULL;

  cs_real_t *gweight = NULL;

  /*==========================================================================
    1. Initialization
    ==========================================================================*/

  if (init >= 1) {
#   pragma omp parallel for
    for (cs_lnum_t ii = 0; ii < n_cells_ext; ii++) {
      diverg[ii] = 0.;
    }
  } else if (init == 0 && n_cells_ext > n_cells) {
#   pragma omp parallel for if(n_cells_ext - n_cells > CS_THR_MIN)
    for (cs_lnum_t ii = n_cells+0; ii < n_cells_ext; ii++) {
      diverg[ii] = 0.;
    }
  } else if (init != 0) {
    bft_error(__FILE__, __LINE__, 0,
              _("invalid value of init"));
  }

  /* Use iterative gradient */

  cs_halo_type_t halo_type = CS_HALO_STANDARD;
  cs_gradient_type_t gradient_type = CS_GRADIENT_GREEN_ITER;

  if (imrgra < 0)
    imrgra = 0;

  cs_gradient_type_by_imrgra(imrgra,
                             &gradient_type,
                             &halo_type);

  if (f_id != -1) {
    f = cs_field_by_id(f_id);

    int df_limiter_id
      = cs_field_get_key_int(f, cs_field_key_id("diffusion_limiter_id"));
    if (df_limiter_id > -1)
      df_limiter = cs_field_by_id(df_limiter_id)->val;


    snprintf(var_name, 63, "%s", f->name);
  }
  else
    strncpy(var_name, "[cell mass flux divergence update]", 63);
  var_name[63] = '\0';

  /* Porosity fields */
  cs_field_t *fporo = cs_field_by_name_try("porosity");
  cs_field_t *ftporo = cs_field_by_name_try("tensorial_porosity");

  cs_real_t *porosi = NULL;
  cs_real_6_t *porosf = NULL;

  if (cs_glob_porous_model == 1 || cs_glob_porous_model == 2) {
    porosi = fporo->val;
    if (ftporo != NULL) {
      porosf = (cs_real_6_t *)ftporo->val;
    }
  }

  /* Handle parallelism and periodicity */

  if (halo != NULL)
    cs_halo_sync_var(halo, halo_type, pvar);

  /*==========================================================================
    2. Update mass flux without reconstruction technics
    ==========================================================================*/

  if (nswrgp <= 1) {

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double flux = i_visc[face_id]*(pvar[ii] - pvar[jj]);
          diverg[ii] += flux;
          diverg[jj] -= flux;

        }
      }
    }

    /* Mass flow though boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];
          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pvar[ii];

          double flux = b_visc[face_id]*pfac;
          diverg[ii] += flux;

        }
      }
    }

  }

  /*==========================================================================
    3. Update mass flux with reconstruction technics
    ==========================================================================*/

  if (nswrgp > 1) {

    viscce = NULL;
    w2 = NULL;

    /* Without porosity */
    if (porosi == NULL) {
      viscce = viscel;

      /* With porosity */
    } else if (porosi != NULL && porosf == NULL) {
      BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
      for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
        for (int isou = 0; isou < 6; isou++) {
          w2[cell_id][isou] = porosi[cell_id]*viscel[cell_id][isou];
        }
      }
      viscce = w2;

      /* With tensorial porosity */
    } else if (porosi != NULL && porosf != NULL) {
      BFT_MALLOC(w2, n_cells_ext, cs_real_6_t);
      for (cs_lnum_t cell_id = 0; cell_id < n_cells; cell_id++) {
        cs_math_sym_33_product(porosf[cell_id],
                               viscel[cell_id],
                               w2[cell_id]);
      }
      viscce = w2;
    }

    /* ---> Periodicity and parallelism treatment of symmetric tensors */

    if (halo != NULL) {
      cs_halo_sync_var_strided(halo, CS_HALO_STANDARD, (cs_real_t *)viscce, 6);

      if (m->n_init_perio > 0)
        cs_halo_perio_sync_var_sym_tens(halo,
                                        CS_HALO_STANDARD,
                                        (cs_real_t *)viscce);
    }

    /* Allocate a work array for the gradient calculation */
    BFT_MALLOC(grad, n_cells_ext, cs_real_3_t);

    /* Compute gradient */
    if (iwgrp > 0) {
      gweight = (cs_real_t *)viscce;
      if (halo != NULL) {
        cs_halo_sync_var_strided(halo, halo_type, gweight, 6);
        if (cs_glob_mesh->n_init_perio > 0)
          cs_halo_perio_sync_var_sym_tens(halo, halo_type, gweight);
      }
    }

    else if (f_id > -1) {
      /* Get the calculation option from the field */
      int key_cal_opt_id = cs_field_key_id("var_cal_opt");
      cs_var_cal_opt_t var_cal_opt;
      cs_field_get_key_struct(f, key_cal_opt_id, &var_cal_opt);
      if (f->type & CS_FIELD_VARIABLE && var_cal_opt.iwgrec == 1) {
        if (var_cal_opt.idifft > 0) {
          int key_id = cs_field_key_id("gradient_weighting_id");
          int diff_id = cs_field_get_key_int(f, key_id);
          if (diff_id > -1) {
            cs_field_t *weight_f = cs_field_by_id(diff_id);
            gweight = weight_f->val;
            w_stride = weight_f->dim;
            cs_field_synchronize(weight_f, halo_type);
          }
        }
      }
    }

    /* Compute gradient */
    cs_gradient_scalar_synced_input(var_name,
                                    gradient_type,
                                    halo_type,
                                    inc,
                                    recompute_cocg,
                                    nswrgp,
                                    tr_dim,
                                    iphydp,
                                    w_stride,
                                    iwarnp,
                                    imligp,
                                    epsrgp,
                                    climgp,
                                    frcxt,
                                    coefap,
                                    coefbp,
                                    pvar,
                                    gweight, /* Weighted gradient */
                                    NULL, /* internal coupling */
                                    grad);

    /* Mass flow through interior faces */

    for (int g_id = 0; g_id < n_i_groups; g_id++) {
#     pragma omp parallel for
      for (int t_id = 0; t_id < n_i_threads; t_id++) {
        for (cs_lnum_t face_id = i_group_index[(t_id*n_i_groups + g_id)*2];
             face_id < i_group_index[(t_id*n_i_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = i_face_cells[face_id][0];
          cs_lnum_t jj = i_face_cells[face_id][1];

          double pi = pvar[ii];
          double pj = pvar[jj];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(CS_MIN(df_limiter[ii], df_limiter[jj]), 0.);


          /* Recompute II" and JJ"
             ----------------------*/

          cs_real_t visci[3][3], viscj[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          cs_real_t fikdvi = weighf[face_id][0];

          /* II" = IF + FI" */

          double diippf[3], djjppf[3];

          for (int i = 0; i < 3; i++) {
            diippf[i] = i_face_cog[face_id][i]-cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*i_face_normal[face_id][0]
                               + visci[1][i]*i_face_normal[face_id][1]
                               + visci[2][i]*i_face_normal[face_id][2] );
          }

          viscj[0][0] = viscce[jj][0];
          viscj[1][1] = viscce[jj][1];
          viscj[2][2] = viscce[jj][2];
          viscj[1][0] = viscce[jj][3];
          viscj[0][1] = viscce[jj][3];
          viscj[2][1] = viscce[jj][4];
          viscj[1][2] = viscce[jj][4];
          viscj[2][0] = viscce[jj][5];
          viscj[0][2] = viscce[jj][5];

          /* FJ.Kj.S / ||Kj.S||^2 */
          double fjkdvi = weighf[face_id][1];

          /* JJ" = JF + FJ" */
          for (int i = 0; i < 3; i++) {
            djjppf[i] = i_face_cog[face_id][i]-cell_cen[jj][i]
                      + fjkdvi*( viscj[0][i]*i_face_normal[face_id][0]
                               + viscj[1][i]*i_face_normal[face_id][1]
                               + viscj[2][i]*i_face_normal[face_id][2] );
          }

          /* p in I" and J" */
          double pipp = pi + bldfrp*( grad[ii][0]*diippf[0]
                                    + grad[ii][1]*diippf[1]
                                    + grad[ii][2]*diippf[2]);
          double pjpp = pj + bldfrp*( grad[jj][0]*djjppf[0]
                                    + grad[jj][1]*djjppf[1]
                                    + grad[jj][2]*djjppf[2]);

          double flux = i_visc[face_id]*(pipp - pjpp);

          diverg[ii] += flux;
          diverg[jj] -= flux;

        }
      }
    }

    /* Mass flow though boundary faces */

    for (int g_id = 0; g_id < n_b_groups; g_id++) {
#     pragma omp parallel for if(m->n_b_faces > CS_THR_MIN)
      for (int t_id = 0; t_id < n_b_threads; t_id++) {
        for (cs_lnum_t face_id = b_group_index[(t_id*n_b_groups + g_id)*2];
             face_id < b_group_index[(t_id*n_b_groups + g_id)*2 + 1];
             face_id++) {

          cs_lnum_t ii = b_face_cells[face_id];

          double pi = pvar[ii];

          cs_real_t bldfrp = (cs_real_t) ircflp;
          /* Local limitation of the reconstruction */
          if (df_limiter != NULL && ircflp > 0)
            bldfrp = CS_MAX(df_limiter[ii], 0.);

          /* Recompute II"
             --------------*/

          cs_real_t visci[3][3];

          visci[0][0] = viscce[ii][0];
          visci[1][1] = viscce[ii][1];
          visci[2][2] = viscce[ii][2];
          visci[1][0] = viscce[ii][3];
          visci[0][1] = viscce[ii][3];
          visci[2][1] = viscce[ii][4];
          visci[1][2] = viscce[ii][4];
          visci[2][0] = viscce[ii][5];
          visci[0][2] = viscce[ii][5];

          /* IF.Ki.S / ||Ki.S||^2 */
          double fikdvi = weighb[face_id];

          double diippf[3];

          /* II" = IF + FI" */
          for (int i = 0; i < 3; i++) {
            diippf[i] = b_face_cog[face_id][i] - cell_cen[ii][i]
                      - fikdvi*( visci[0][i]*b_face_normal[face_id][0]
                               + visci[1][i]*b_face_normal[face_id][1]
                               + visci[2][i]*b_face_normal[face_id][2] );
          }

          double pipp = pi + bldfrp*(  grad[ii][0]*diippf[0]
                                     + grad[ii][1]*diippf[1]
                                     + grad[ii][2]*diippf[2]);


          double pfac = inc*cofafp[face_id] + cofbfp[face_id]*pipp;

          double flux = b_visc[face_id]*pfac;
          diverg[ii] += flux;

        }
      }
    }

    /* Free memory */
    BFT_FREE(grad);
    BFT_FREE(w2);

  }

}

/*----------------------------------------------------------------------------*/

END_C_DECLS
