Op_Conv_kschemas_VEF.cpp

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#include <Op_Conv_kschemas_VEF.h>
#include <Periodique.h>
#include <Neumann_sortie_libre.h>
 
Implemente_base(Op_Conv_kschemas_VEF,"Op_Conv_kschemas_VEF_P1NC",Op_Conv_VEF_base);
 
 
Sortie& Op_Conv_kschemas_VEF::printOn(Sortie& s ) const
{
  return s << que_suis_je() ;
}
 
Entree& Op_Conv_kschemas_VEF::readOn(Entree& s )
{
  return s ;
}
 
void Op_Conv_kschemas_VEF::associer(const Domaine_dis_base& domaine_dis, const Domaine_Cl_dis_base& domaine_cl_dis, const Champ_Inc_base& ch)
{
  // CCa le 28/05/99 The Kquick scheme does not work in parallel!!
  if (Process::is_parallel())
    {
      Cerr << "WARNING: kquick scheme does not work in parallel !!!" << finl;
      exit();
    }
 
  Op_Conv_VEF_base::associer(domaine_dis, domaine_cl_dis, ch);
}
 
 
//////////////////////////////////////////////////////////////
//   Functions for the k-schemes.
////////////////////////////////////////////////////////////////
 
// convkschemas : utility function for convection
 
void convkschemas(const double K, const int ncomp, int dimension, const int poly ,
                  const int poly1, const int poly2,const int jel0,
                  const int jel1,const double psc ,const DoubleTab& tab1 ,
                  DoubleVect& fluent, DoubleVect& flux,
                  const DoubleVect& rx0, const DoubleTab& gradient_elem )
{
 
  int comp,amont,i,elem1,elem2;
  double CF,UTC,deltat0,deltat1,deltat;
  DoubleVect rx(dimension);
  deltat0 = 0.;
  deltat1 = 0.;
 
  ////////////////////////////////////////////////////////////////////////
  // Test on boundaries
  ////////////////////////////////////////////////////////////////////////
  if ((poly1==-1) || (poly2==-1))
    {
      if (psc >= 0)
        {
          amont = jel0;
          fluent[jel1] += psc;
        }
      else
        {
          amont = jel1;
          fluent[jel0] -= psc;
        }
 
      for (comp=0; comp<ncomp; comp++)
        flux(comp) = tab1(amont,comp);
 
    }
  else
    {
      if (psc >= 0)
        {
          amont = jel0;
          rx = rx0;
          elem1 = poly;
          elem2 = poly1;
          fluent(jel1)  += psc;
        }
      else
        {
          amont = jel1;
          rx = rx0;
          rx *= -1.;
          elem1 = poly;
          elem2 = poly2;
          fluent(jel0)  -= psc;
        }
 
      for (comp=0; comp<ncomp; comp++)
        {
          deltat0 = deltat1 = 0.0;
          flux(comp) = tab1(amont,comp);
          //Cerr << " flux(" << comp << ") ie phiamont= " <<  flux(comp) << finl;
 
          for (i=0; i<dimension; i++)
            {
              deltat0 += gradient_elem(elem1,comp,i)*rx(i);
              deltat1 += gradient_elem(elem2,comp,i)*rx(i);
            }
 
          if (K == 0.5)
            {
              deltat = deltat0 + deltat1;
 
              if  (std::fabs(deltat) <= 1.e-5)
                {
                  CF = 0.125;
                }
              else
                {
                  UTC = deltat1 / deltat;
 
                  if ( (UTC <= -1.) || (UTC >= 1.5) )      CF = 0.125;
                  else if ((UTC > -1.) && (UTC <= 0.))     CF = 0.5 + 0.375*UTC;
                  else if ((UTC > 0.) && (UTC <= 0.25))    CF = 0.5 - 0.625*sqrt(UTC);
                  else if ((UTC > 0.25) && (UTC < 1.5 ))   CF = 0.25* std::fabs(UTC - 1.);
                  else
                    {
                      CF=0.;
                      Process::exit();
                    }
                }
              // Compute the flux
              flux(comp) += (0.5 - CF)*deltat0 + CF*deltat1 ;
              //Cerr << " flux(" << comp << ")= " <<  flux(comp) << finl;
            }
          else
            {
              // Compute the flux
              flux(comp) += 0.25*((1.+K)*deltat0 + (1.-K)*deltat1) ;
            }
        }
 
    }
}
 
//////////////////////////////////////////////////////////////////////////
// Procedure AJOUTER
/////////////////////////////////////////////////////////////////////////
 
DoubleTab& Op_Conv_kschemas_VEF::ajouter(const DoubleTab& transporte,
                                         DoubleTab& resu) const
{
  const Domaine_Cl_VEF& domaine_Cl_VEF = la_zcl_vef.valeur();
  const Domaine_VEF& domaine_VEF = le_dom_vef.valeur();
  const DoubleVect& porosite_face = equation().milieu().porosite_face();
  const Champ_Inc_base& la_vitesse=vitesse_.valeur();
  const IntTab& elem_faces = domaine_VEF.elem_faces();
  const DoubleTab& face_normales = domaine_VEF.face_normales();
  const auto& facette_normales = domaine_VEF.facette_normales();
  const Domaine& domaine = domaine_VEF.domaine();
  const int nb_faces = domaine_VEF.nb_faces();
  const int nfa7 = domaine_VEF.type_elem().nb_facette();
  const int nb_elem = domaine_VEF.nb_elem();
  const int nb_elem_tot = domaine_VEF.nb_elem_tot();
  const IntVect& rang_elem_non_std = domaine_VEF.rang_elem_non_std();
  const IntTab& face_voisins = domaine_VEF.face_voisins();
  const DoubleVect& volumes = domaine_VEF.volumes();
  const DoubleTab& xv = domaine_VEF.xv();
  const DoubleTab& xg = domaine_VEF.xp();
  const DoubleTab& coord = domaine.coord_sommets();
  int premiere_face_int = domaine_VEF.premiere_face_int();
  const IntTab& les_Polys = domaine.les_elems();
 
  const DoubleTab& normales_facettes_Cl = domaine_Cl_VEF.normales_facettes_Cl();
 
  int nfac = domaine.nb_faces_elem();
  int nsom = domaine.nb_som_elem();
  int nb_som_facette = domaine.type_elem()->nb_som_face();
 
  // For the convection treatment, standard polyhedra (not "seeing" boundary conditions)
  // are distinguished from non-standard polyhedra (having at least one boundary face).
  // A standard polyhedron has n facets on which the convection scheme is applied.
  // For a non-standard polyhedron with Dirichlet boundary conditions, part of its
  // facets are carried by the boundary faces.
  // In short, for a polyhedron the convection treatment depends on the type
  // (triangle, tetrahedron ...) and the number of Dirichlet faces.
 
  double psc;
  int poly,poly1,poly2,face_adj,fa7,i,j,n_bord;
  int num_face, rang ,itypcl;
  int num10,num20,num3,num_som;
 
  // MODIF SB su 10/09/03
  // For the following 3 elements, there are as many vertices as faces
  // making up the geometric element.
  // Problem with hexahedra: 8 vertices and 6 faces, so using the array
  // face[i] no longer works.
  // The method retained to avoid computing velocity at vertices without
  // the shape functions is therefore not usable for hexahedra,
  // where the Face=>vertices array exists but not its inverse.
  // Too costly; porosity extension to hexahedra is not done for now.
 
  int istetra=0;
  const Elem_VEF_base& type_elemvef= domaine_VEF.type_elem();
  Nom nom_elem=type_elemvef.que_suis_je();
  if ((nom_elem=="Tetra_VEF")||(nom_elem=="Tri_VEF")) istetra=1;
 
  const int ncomp_ch_transporte= transporte.line_size();
  int fac,elem1,elem2,comp0;
  int nb_faces_ = domaine_VEF.nb_faces();
  IntVect face(nfac);
 
  DoubleVect flux(ncomp_ch_transporte);
  DoubleVect fluxsom(ncomp_ch_transporte);
  DoubleVect fluxg(ncomp_ch_transporte);
 
  // Special treatment for periodic faces
  int nb_faces_perio = 0;
  for (n_bord=0; n_bord<domaine_VEF.nb_front_Cl(); n_bord++)
    {
      const Cond_lim& la_cl = domaine_Cl_VEF.les_conditions_limites(n_bord);
      if (sub_type(Periodique,la_cl.valeur()))
        {
          const Front_VF& le_bord = ref_cast(Front_VF,la_cl->frontiere_dis());
          int num1 = le_bord.num_premiere_face();
          int num2 = num1 + le_bord.nb_faces();
          for (num_face=num1; num_face<num2; num_face++)
            nb_faces_perio++;
        }
    }
 
  DoubleTab tab(nb_faces_perio,ncomp_ch_transporte);
 
  nb_faces_perio=0;
  for (n_bord=0; n_bord<domaine_VEF.nb_front_Cl(); n_bord++)
    {
      const Cond_lim& la_cl = domaine_Cl_VEF.les_conditions_limites(n_bord);
      if (sub_type(Periodique,la_cl.valeur()))
        {
          const Front_VF& le_bord = ref_cast(Front_VF,la_cl->frontiere_dis());
          int num1 = le_bord.num_premiere_face();
          int num2 = num1 + le_bord.nb_faces();
          for (num_face=num1; num_face<num2; num_face++)
            {
              for (int comp=0; comp<ncomp_ch_transporte; comp++)
                tab(nb_faces_perio,comp) = resu(num_face,comp);
              nb_faces_perio++;
            }
        }
    }
 
 
  ///////////////////////////////////////////////////////////////////////////////////////////////
  //                        <
  // gradient computation;  < [ Ujp*np/vol(j) ]
  //                         j
  ////////////////////////////////////////////////////////////////////////////////////////////////
  DoubleTab gradient_elem(0, ncomp_ch_transporte, dimension);
  domaine_VEF.domaine().creer_tableau_elements(gradient_elem);
  // Loop over faces
 
 
  for (fac=0; fac< premiere_face_int; fac++)
    {
      elem1=face_voisins(fac,0);
      if(ncomp_ch_transporte==1)
        for (i=0; i<dimension; i++)
          {
            gradient_elem(elem1, 0, i) +=
              face_normales(fac,i)*transporte(fac);
          }
      else
        for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
          for (i=0; i<dimension; i++)
            gradient_elem(elem1, comp0, i) +=
              face_normales(fac,i)*transporte(fac,comp0);
      // dUcomp/dXi
    } // end of for faces
 
  for (; fac<nb_faces_; fac++)
    {
      elem1=face_voisins(fac,0);
      elem2=face_voisins(fac,1);
      if(ncomp_ch_transporte==1)
        for (i=0; i<dimension; i++)
          {
            gradient_elem(elem1, 0, i) +=
              face_normales(fac,i)*transporte(fac);
            gradient_elem(elem2, 0, i) -=
              face_normales(fac,i)*transporte(fac);
          }
      else
        for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
          for (i=0; i<dimension; i++)
            {
              gradient_elem(elem1, comp0, i) +=
                face_normales(fac,i)*transporte(fac,comp0);
              gradient_elem(elem2, comp0, i) -=
                face_normales(fac,i)*transporte(fac,comp0);
            }
      // dUcomp/dXi
    } // end of for faces
 
  for (int elem=0; elem<nb_elem; elem++)
    for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
      for (i=0; i<dimension; i++)
        gradient_elem(elem,comp0,i) /= volumes(elem);
 
  gradient_elem.echange_espace_virtuel();
 
  ////////////////////////////////////////////////////////////////////////////////////
  // We have gradient_elem per element
  ////////////////////////////////////////////////////////////////////////////////////
 
  DoubleVect vs(dimension);
  DoubleVect vc(dimension);
  DoubleTab vsom(nsom,dimension);
  DoubleVect cc(dimension);
  double xm;
 
  // Reset the array used for
  // computing the stability time step
  fluent_ = 0;
 
  // Non-standard polyhedra are grouped into 2 sets in Domaine_VEF:
  //  - boundary and joint polyhedra
  //  - boundary and non-joint polyhedra
  // Polyhedra are processed in the order in which they appear in the domain
 
  //////////////////////////////////////////////////////////////////////////////////////
  // loop over polyhedra
  //////////////////////////////////////////////////////////////////////////////////////
  const IntTab& KEL=domaine_VEF.type_elem().KEL();
  for (poly=0; poly<nb_elem; poly++)
    {
      rang = rang_elem_non_std(poly);
      if (rang==-1)
        itypcl=0;
      else
        itypcl=domaine_Cl_VEF.type_elem_Cl(rang);
 
      // compute the face indices of the polyhedron
      for (face_adj=0; face_adj<nfac; face_adj++)
        face(face_adj)= elem_faces(poly,face_adj);
 
      int scom;
      DoubleVect rx0(dimension);
 
      // compute velocity at the vertices of the polyhedra
      for (j=0; j<dimension; j++)
        {
          vs(j) = la_vitesse.valeurs()(face(0),j)*porosite_face(face(0));
          for (i=1; i<nfac; i++)
            vs(j)+= la_vitesse.valeurs()(face(i),j)*porosite_face(face(i));
        }
 
      //int ncomp;
      if (istetra==1)
        {
          for (j=0; j<nsom; j++)
            {
              for (int ncomp=0; ncomp<Objet_U::dimension; ncomp++)
                vsom(j,ncomp) =vs[ncomp] - Objet_U::dimension*la_vitesse.valeurs()(face[j],ncomp)*porosite_face(face[j]);
            }
        }
      else
        {
          // to be valid with hexahedra
          // Use the shape functions implemented in class Champs_P1_impl or Champs_Q1_impl
          //int ncomp;
          for (j=0; j<nsom; j++)
            {
              num_som = domaine.sommet_elem(poly,j);
              for (int ncomp=0; ncomp<dimension; ncomp++)
                {
                  vsom(j,ncomp) = la_vitesse.valeur_a_sommet_compo(num_som,poly,ncomp);
                }
            }
        }
      // compute the velocity at the centre of gravity
      domaine_VEF.type_elem().calcul_vc(face,vc,vs,vsom,vitesse(),itypcl,porosite_face);
 
      // Loop over facets of the non-standard polyhedron:
      for (fa7=0; fa7<nfa7; fa7++)
        {
          //Cerr << "the facet being studied is " << fa7 << finl;
          // fa7 separates num1 and num2. num3 is the third face (2D).
 
          num10 = face(KEL(0,fa7));
          num20 = face(KEL(1,fa7));
          num3 = face(KEL(2,fa7));
 
          // Determine the neighbouring elements at faces num1 and num2
 
          poly1 = face_voisins(num10,0);
          if (poly1==poly)
            poly1 = face_voisins(num10,1);
 
          poly2 = face_voisins(num20,0);
          if (poly2==poly)
            poly2 = face_voisins(num20,1);
 
          scom = les_Polys(poly,KEL(2,fa7));
 
          // compute rx0, distance between the midpoints of 'num i'
 
          for (i=0; i<dimension; i++)
            rx0(i) = xv(num20,i)-xv(num10,i);
 
          // facet normals
 
          if (rang==-1)
            for (i=0; i<dimension; i++)
              cc[i] = facette_normales(poly, fa7, i);
          else
            for (i=0; i<dimension; i++)
              cc[i] = normales_facettes_Cl(rang,fa7,i);
 
          /////////////////////////////////////////////////////////////////////////
          // Process the point for which velocity = 0.5*(vertex_velocity + midpoint_velocity)
          /////////////////////////////////////////////////////////////////////////
 
          for (i=0; i<nb_som_facette-1; i++)
            {
              //////////////////////////////////////////////////////////////////////////
              //Determination of PhiIJ at the midpoint between the vertex and the center of num3
              /////////////////////////////////////////////////////////////////////////
 
              psc = 0;
              for (j=0; j<dimension; j++)
                psc+=((vsom(KEL(i+2,fa7),j) + la_vitesse.valeurs()(num3,j) * porosite_face(num3)))*cc[j];
              psc *=0.5;
              convkschemas(K,ncomp_ch_transporte,dimension,poly,poly1,poly2,num10,num20,psc,transporte,
                           fluent_,flux,rx0,gradient_elem);
 
              ////////////////////////////////////////////////////////////////////////////////////////////////////////
              //Gradient limiter. Computed at the same time as the flux.
              // gradient(K0) = teta*gradient(K0)+ (1-teta)*gradient(K1 or K2)
              ////////////////////////////////////////////////////////////////////////////////////////////////////////
 
              double teta = 0.5;
 
              /////////////////////////////////////////////////////////////////////////
              // Process the vertices that are also vertices of the polyhedron
              /////////////////////////////////////////////////////////////////////////
 
              // XXX XXX XXX : Attention : we can not factorize more... the code is not the same
              if (ncomp_ch_transporte == 1)
                {
                  for (j=0; j<dimension; j++)
                    {
                      xm = 0.5 *(coord(scom,j)+xv(num3,j));
                      if (psc >= 0)
                        {
                          if (poly1==-1)
                            fluxsom(0) += gradient_elem(poly,0,j)*(coord(scom,j)-xm);
                          else
                            fluxsom(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly1,0,j))*(coord(scom,j)-xm);
                        }
                      else
                        {
                          if (poly2==-1)
                            fluxsom(0) += gradient_elem(poly,0,j)*(coord(scom,j)-xm);
                          else
                            fluxsom(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly2,0,j))*(coord(scom,j)-xm);
                        }
                    }
                  fluxsom(0) += flux(0);
                  fluxsom(0) *= psc;
                }
              else
                {
                  for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                    {
                      fluxsom(comp0) = flux(comp0);
                      for (j=0; j<dimension; j++)
                        {
                          xm = 0.5 *(coord(scom,j)+xv(num3,j));
                          if (psc >= 0)
                            {
                              if (poly1==-1)
                                fluxsom(comp0) += gradient_elem(poly,comp0,j)*(coord(scom,j)-xm);
                              else
                                fluxsom(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly1,comp0,j))*(coord(scom,j)-xm);
                            }
                          else
                            {
                              if (poly2==-1)
                                fluxsom(comp0) += gradient_elem(poly,comp0,j)*(coord(scom,j)-xm);
                              else
                                fluxsom(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly2,comp0,j))*(coord(scom,j)-xm);
                            }
                        }
                      fluxsom(comp0) *= psc;
                    }
                }
 
              ////////////////////////////////////////////////////////////////////////////
              // process the centre of gravity
              ////////////////////////////////////////////////////////////////////////////
 
              // XXX XXX XXX : Attention : we can not factorize more... the code is not the same
              if (ncomp_ch_transporte == 1)
                {
                  for (j=0; j<dimension; j++)
                    {
                      xm = 0.5 *(coord(scom,j)+xv(num3,j));
                      if (psc >= 0)
                        {
                          if (poly1==-1)
                            fluxg(0) += gradient_elem(poly,0,j)*(xg(poly,j)-xm);
                          else
                            fluxg(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly1,0,j))*(xg(poly,j)-xm);
                        }
 
                      else
                        {
                          if (poly2==-1)
                            fluxg(0) += gradient_elem(poly,0,j)*(xg(poly,j)-xm);
                          else
                            fluxg(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly2,0,j))*(xg(poly,j)-xm);
                        }
                    }
 
                  fluxg(0) += flux(0);
                  fluxg(0) *= psc;
                }
              else
                {
                  for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                    {
                      fluxg(comp0) = flux(comp0);
                      for (j=0; j<dimension; j++)
                        {
                          xm = 0.5 *(coord(scom,j)+xv(num3,j));
                          if (psc >= 0)
                            {
                              if (poly1==-1)
                                fluxg(comp0) += gradient_elem(poly,comp0,j)*(xg(poly,j)-xm);
                              else
                                fluxg(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly1,comp0,j))*(xg(poly,j)-xm);
                            }
 
                          else
                            {
                              if (poly2==-1)
                                fluxg(comp0) += gradient_elem(poly,comp0,j)*(xg(poly,j)-xm);
                              else
                                fluxg(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly2,comp0,j))*(xg(poly,j)-xm);
                            }
                        }
                      fluxg(comp0) *= psc;
                    }
                }
              //////////////////////////////////////////////////////////////////////////////
              // Integration of u.n.flux
              /////////////////////////////////////////////////////////////////////////////
              for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                {
                  resu(num10,comp0) -= ( 0.5*(fluxsom(comp0)+fluxg(comp0)) );
                  resu(num20,comp0) += ( 0.5*(fluxsom(comp0)+fluxg(comp0)) );
                }
            }
        }
    } // end of the loop
 
  // Process joint elements of thickness 1
  for (poly=0; poly<nb_elem_tot; poly++)
    {
      // Check if a face of the polyhedron is a joint face
      for (face_adj=0; face_adj<nfac; face_adj++)
        if(face_adj<nb_faces) break;
      if(face_adj<nfac)
        {
          rang = rang_elem_non_std(poly);
          if (rang==-1)
            itypcl=0;
          else
            itypcl=domaine_Cl_VEF.type_elem_Cl(rang);
 
          // compute the face indices of the polyhedron
          for (face_adj=0; face_adj<nfac; face_adj++)
            {
              face(face_adj)= elem_faces(poly,face_adj);
              //Cerr << "the faces of the element are: " << face(face_adj) << finl;
            }
 
          int scom;
          DoubleVect rx0(dimension);
 
          // compute velocity at the vertices of the polyhedra
          for (j=0; j<dimension; j++)
            {
              vs(j) = la_vitesse.valeurs()(face(0),j)*porosite_face(face(0));
              for (i=1; i<nfac; i++)
                vs(j)+= la_vitesse.valeurs()(face(i),j)*porosite_face(face(j));
            }
          int ncomp;
          for (j=0; j<nsom; j++)
            {
              num_som = domaine.sommet_elem(poly,j);
              for (ncomp=0; ncomp<dimension; ncomp++)
                vsom(j,ncomp) = la_vitesse.valeur_a_sommet_compo(num_som,poly,ncomp);
            }
          // compute the velocity at the centre of gravity
 
          domaine_VEF.type_elem().calcul_vc(face,vc,vs,vsom,vitesse(),itypcl,porosite_face);
 
 
          // Loop over facets of the non-standard polyhedron:
 
          for (fa7=0; fa7<nfa7; fa7++)
            {
              //Cerr << "the facet being studied is " << fa7 << finl;
              // fa7 separates num1 and num2. num3 is the third face (2D).
 
              num10 = face(KEL(0,fa7));
              num20 = face(KEL(1,fa7));
              num3 = face(KEL(2,fa7));
 
              // Determine the neighbouring elements at faces num1 and num2
 
              poly1 = face_voisins(num10,0);
              if (poly1==poly)
                {
                  poly1 = face_voisins(num10,1);
                }
 
              poly2 = face_voisins(num20,0);
              if (poly2==poly)
                {
                  poly2 = face_voisins(num20,1);
                }
 
              scom = les_Polys(poly,KEL(2,fa7));
 
              // compute rx0, distance between the midpoints of 'num i'
 
              for (i=0; i<dimension; i++)
                rx0(i) = xv(num20,i)-xv(num10,i);
 
              // facet normals
 
              if (rang==-1)
                for (i=0; i<dimension; i++)
                  cc[i] = facette_normales(poly, fa7, i);
              else
                for (i=0; i<dimension; i++)
                  cc[i] = normales_facettes_Cl(rang,fa7,i);
 
              /////////////////////////////////////////////////////////////////////////
              // Process the point where velocity = 0.5(vitsommet + vitmilieu)
              /////////////////////////////////////////////////////////////////////////
 
              for (i=0; i<nb_som_facette-1; i++)
                {
                  //////////////////////////////////////////////////////////////////////////
                  //Determine PhiIJ at the midpoint between the vertex and the midpoint of num3
                  /////////////////////////////////////////////////////////////////////////
 
                  psc = 0;
                  for (j=0; j<dimension; j++)
                    psc+=((vsom(KEL(i+2,fa7),j) + la_vitesse.valeurs()(num3,j) * porosite_face(num3)))*cc[j];
                  psc *=0.5;
                  convkschemas(K,ncomp_ch_transporte,dimension,poly,poly1,poly2,num10,num20,psc,transporte,
                               fluent_,flux,rx0,gradient_elem);
 
 
                  ////////////////////////////////////////////////////////////////////////////////////////////////////////
                  //Gradient limiter. Computed at the same time as the flux.
                  // gradient(K0) = teta*gradient(K0)+ (1-teta)*gradient(K1 or K2)
                  ////////////////////////////////////////////////////////////////////////////////////////////////////////
 
                  double teta = 0.5;
 
                  /////////////////////////////////////////////////////////////////////////
                  // Process the vertices that are also vertices of the polyhedron
                  /////////////////////////////////////////////////////////////////////////
 
                  // XXX XXX XXX : Attention : we can not factorize more... the code is not the same
                  if (ncomp_ch_transporte == 1)
                    {
                      for (j=0; j<dimension; j++)
                        {
                          xm = 0.5 *(coord(scom,j)+xv(num3,j));
                          if (psc >= 0)
                            {
                              if (poly1==-1)
                                fluxsom(0) += gradient_elem(poly,0,j)*(coord(scom,j)-xm);
                              else
                                fluxsom(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly1,0,j))*(coord(scom,j)-xm);
                            }
                          else
                            {
                              if (poly2==-1)
                                fluxsom(0) += gradient_elem(poly,0,j)*(coord(scom,j)-xm);
                              else
                                fluxsom(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly2,0,j))*(coord(scom,j)-xm);
                            }
                        }
                      fluxsom(0) += flux(0);
                      fluxsom(0) *= psc;
                    }
                  else
                    {
                      for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                        {
                          fluxsom(comp0) = flux(comp0);
                          for (j=0; j<dimension; j++)
                            {
                              xm = 0.5 *(coord(scom,j)+xv(num3,j));
                              if (psc >= 0)
                                {
                                  if (poly1==-1)
                                    fluxsom(comp0) += gradient_elem(poly,comp0,j)*(coord(scom,j)-xm);
                                  else
                                    fluxsom(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly1,comp0,j))*(coord(scom,j)-xm);
                                }
                              else
                                {
                                  if (poly2==-1)
                                    fluxsom(comp0) += gradient_elem(poly,comp0,j)*(coord(scom,j)-xm);
                                  else
                                    fluxsom(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly2,comp0,j))*(coord(scom,j)-xm);
                                }
                            }
                          fluxsom(comp0) *= psc;
                        }
                    }
 
                  ////////////////////////////////////////////////////////////////////////////
                  // Process the center of gravity
                  ////////////////////////////////////////////////////////////////////////////
 
                  // XXX XXX XXX : Attention : we can not factorize more... the code is not the same
                  if (ncomp_ch_transporte == 1)
                    {
                      for (j=0; j<dimension; j++)
                        {
                          xm = 0.5 *(coord(scom,j)+xv(num3,j));
                          if (psc >= 0)
                            {
                              if (poly1==-1)
                                fluxg(0) += gradient_elem(poly,0,j)*(xg(poly,j)-xm);
                              else
                                fluxg(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly1,0,j))*(xg(poly,j)-xm);
                            }
                          else
                            {
                              if (poly2==-1)
                                fluxg(0) += gradient_elem(poly,0,j)*(xg(poly,j)-xm);
                              else
                                fluxg(0) += (teta*gradient_elem(poly,0,j) + (1.- teta)*gradient_elem(poly2,0,j))*(xg(poly,j)-xm);
                            }
                        }
                      fluxg(0) += flux(0);
                      fluxg(0) *= psc;
                    }
                  else
                    {
                      for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                        {
                          fluxg(comp0) = flux(comp0);
                          for (j=0; j<dimension; j++)
                            {
                              xm = 0.5 *(coord(scom,j)+xv(num3,j));
                              if (psc >= 0)
                                {
                                  if (poly1==-1)
                                    fluxg(comp0) += gradient_elem(poly,comp0,j)*(xg(poly,j)-xm);
                                  else
                                    fluxg(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly1,comp0,j))*(xg(poly,j)-xm);
                                }
                              else
                                {
                                  if (poly2==-1)
                                    fluxg(comp0) += gradient_elem(poly,comp0,j)*(xg(poly,j)-xm);
                                  else
                                    fluxg(comp0) += (teta*gradient_elem(poly,comp0,j) + (1.-teta)*gradient_elem(poly2,comp0,j))*(xg(poly,j)-xm);
                                }
                            }
                          fluxg(comp0) *= psc;
                        }
                    }
 
                  //////////////////////////////////////////////////////////////////////////////
                  // Integration of u.n.flux
                  /////////////////////////////////////////////////////////////////////////////
                  for (comp0=0; comp0<ncomp_ch_transporte; comp0++)
                    {
                      resu(num10,comp0) -= ( 0.5*(fluxsom(comp0)+fluxg(comp0)) );
                      resu(num20,comp0) += ( 0.5*(fluxsom(comp0)+fluxg(comp0)) );
                    }
                }
            }
        }
    } // end of the loop
  int voisine;
  nb_faces_perio = 0;
  double diff1,diff2;
 
  // Dimensioning the array of convective fluxes at the boundary
  // of the computational domain
  DoubleTab& flux_b = flux_bords_;
  flux_b.resize(domaine_VEF.nb_faces_bord(),ncomp_ch_transporte);
  flux_b = 0.;
 
  // Loop over the boundaries to process the boundary conditions
  // a convection term is included for Neumann_sortie_libre boundary conditions only
 
  for (n_bord=0; n_bord<domaine_VEF.nb_front_Cl(); n_bord++)
    {
      const Cond_lim& la_cl = domaine_Cl_VEF.les_conditions_limites(n_bord);
 
      if (sub_type(Neumann_sortie_libre,la_cl.valeur()))
        {
          const Neumann_sortie_libre& la_sortie_libre = ref_cast(Neumann_sortie_libre,la_cl.valeur());
          const Front_VF& le_bord = ref_cast(Front_VF,la_cl->frontiere_dis());
          int num1 = le_bord.num_premiere_face();
          int num2 = num1 + le_bord.nb_faces();
          for (num_face=num1; num_face<num2; num_face++)
            {
              psc =0;
              for (i=0; i<dimension; i++)
                psc += la_vitesse.valeurs()(num_face,i)*face_normales(num_face,i)*porosite_face(num_face);
              if (psc>0)
                for (i=0; i<ncomp_ch_transporte; i++)
                  {
                    resu(num_face,i) -= psc*transporte(num_face,i);
                    flux_b(num_face,i) -= psc*transporte(num_face,i);
                  }
              else
                {
                  for (i=0; i<ncomp_ch_transporte; i++)
                    {
                      resu(num_face,i) -= psc*la_sortie_libre.val_ext(num_face-num1,i);
                      flux_b(num_face,i) -= psc*la_sortie_libre.val_ext(num_face-num1,i);
                    }
                  fluent_(num_face) -= psc;
                }
            }
        }
      else if (sub_type(Periodique,la_cl.valeur()))
        {
          const Periodique& la_cl_perio = ref_cast(Periodique,la_cl.valeur());
          const Front_VF& le_bord = ref_cast(Front_VF,la_cl->frontiere_dis());
          int num1 = le_bord.num_premiere_face();
          int num2 = num1 + le_bord.nb_faces();
          IntVect fait(le_bord.nb_faces());
          fait = 0;
          for (num_face=num1; num_face<num2; num_face++)
            {
              if (fait[num_face-num1] == 0)
                {
                  voisine = la_cl_perio.face_associee(num_face-num1) + num1;
                  for (int comp=0; comp<ncomp_ch_transporte; comp++)
                    {
                      diff1 = resu(num_face,comp)-tab(nb_faces_perio,comp);
                      diff2 = resu(voisine,comp)-tab(nb_faces_perio+voisine-num_face,comp);
                      resu(voisine,comp)  += diff1;
                      resu(num_face,comp) += diff2;
                      flux_b(voisine,comp) += diff1;
                      flux_b(num_face,comp) += diff2;
                    }
                  fait[num_face-num1]= 1;
                  fait[voisine-num1] = 1;
                }
              nb_faces_perio++;
            }
        }
    }
  modifier_flux(*this);
  return resu;
}