Correction_Lubchenko_PolyMAC_MPFA.cpp

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#include <Correction_Lubchenko_PolyMAC_MPFA.h>
#include <Pb_Multiphase.h>
#include <Portance_interfaciale_PolyMAC_MPFA.h>
#include <Portance_interfaciale_base.h>
#include <Op_Diff_Turbulent_PolyMAC_MPFA_Face.h>
#include <Dispersion_bulles_PolyMAC_MPFA.h>
#include <Dispersion_bulles_base.h>
#include <Champ_Face_PolyMAC_MPFA.h>
#include <Milieu_composite.h>
#include <Navier_Stokes_std.h>
#include <Viscosite_turbulente_base.h>
#include <Viscosite_turbulente_multiple.h>
#include <Matrix_tools.h>
#include <Array_tools.h>
#include <Sources_helpers_Multiphase.h>
#include <math.h>
#include <Dispersion_bulles_turbulente_Burns.h>
#include <Domaine_PolyMAC_MPFA.h>
#include <Probleme_base.h>
#include <Champ_Elem_PolyMAC_MPFA.h>
 
Implemente_instanciable(Correction_Lubchenko_PolyMAC_MPFA, "Correction_Lubchenko_Face_PolyMAC_MPFA", Source_base);
// XD Correction_Lubchenko source_base Correction_Lubchenko BRACE not_set
// XD attr beta_lift floattant beta_lift OPT not_set
// XD attr beta_disp floattant beta_disp OPT not_set
 
Sortie& Correction_Lubchenko_PolyMAC_MPFA::printOn(Sortie& os) const
{
  return os;
}
 
Entree& Correction_Lubchenko_PolyMAC_MPFA::readOn(Entree& is)
{
  Param param(que_suis_je());
  param.ajouter("beta_lift", &beta_lift_);
  param.ajouter("beta_disp", &beta_disp_);
  param.ajouter("portee_disp", &portee_disp_);
  param.ajouter("portee_lift", &portee_lift_);
  param.ajouter("use_bif", &use_bif_);
  param.lire_avec_accolades_depuis(is);
 
  //identification des phases
  Pb_Multiphase *pbm = sub_type(Pb_Multiphase, equation().probleme()) ? &ref_cast(Pb_Multiphase, equation().probleme()) : nullptr;
 
  if (!pbm || pbm->nb_phases() == 1)
    Process::exit(que_suis_je() + " : not needed for single-phase flow!");
 
  n_l = find_liquid_phase(*pbm, que_suis_je());
 
  pbm->creer_champ("distance_paroi_globale"); // Besoin de distance a la paroi
 
  return is;
}
 
void Correction_Lubchenko_PolyMAC_MPFA::completer() // We must wait for all readOn's to be sure that the bubble dispersion and lift correlations are created
{
  const Pb_Multiphase& pbm = ref_cast(Pb_Multiphase, equation().probleme());
 
  for (int i = 0 ; i < equation().sources().size() ; i++)
    if sub_type(Portance_interfaciale_PolyMAC_MPFA, equation().sources()(i).valeur())
      correlation_lift_ = ref_cast(Portance_interfaciale_PolyMAC_MPFA, equation().sources()(i).valeur()).correlation();
 
  for (int i = 0 ; i < equation().sources().size() ; i++)
    if sub_type(Dispersion_bulles_PolyMAC_MPFA, equation().sources()(i).valeur())
      correlation_dispersion_ = ref_cast(Dispersion_bulles_PolyMAC_MPFA, equation().sources()(i).valeur()).correlation();
 
  if ( (!correlation_lift_) || (!correlation_dispersion_) )
    Process::exit("Correction_Lubchenko_PolyMAC_MPFA::completer() : a dispersion_bulles and a portance_interfaciale force must be defined !");
 
  if sub_type(Op_Diff_Turbulent_PolyMAC_MPFA_Face, equation().operateur(0).l_op_base()) is_turb = true;
 
  if (!pbm.has_champ("diametre_bulles"))
    Process::exit("Correction_Lubchenko_PolyMAC_MPFA::completer() : a bubble diameter must be defined !");
}
 
 
void Correction_Lubchenko_PolyMAC_MPFA::dimensionner_blocs(matrices_t matrices,
                                                           const tabs_t& semi_impl) const // The necessary dimensionner_bloc is taken care of in the dispersion_bulles_PolyMAC_MPFA and Portance_interfaciale_PolyMAC_MPFA functions
{
}
 
void Correction_Lubchenko_PolyMAC_MPFA::ajouter_blocs(matrices_t matrices, DoubleTab& secmem,
                                                      const tabs_t& semi_impl) const
{
  ajouter_blocs_disp(matrices, secmem, semi_impl);
  ajouter_blocs_lift(matrices, secmem, semi_impl);
  // Le terme source_BIF peut entrainer une mauvaise prédiction des forces normales à la paroi : une correction est mise en place
  if ((use_bif_) && (sub_type(Viscosite_turbulente_multiple, ref_cast(Op_Diff_Turbulent_PolyMAC_MPFA_Face, ref_cast(Navier_Stokes_std, equation().probleme().equation(0)).operateur(0).l_op_base()).correlation())))
    ajouter_blocs_BIF(matrices, secmem, semi_impl);
}
 
void Correction_Lubchenko_PolyMAC_MPFA::ajouter_blocs_disp(matrices_t matrices, DoubleTab& secmem,
                                                           const tabs_t& semi_impl) const
{
  const Pb_Multiphase& pbm = ref_cast(Pb_Multiphase, equation().probleme());
  const Champ_Face_PolyMAC_MPFA& ch = ref_cast(Champ_Face_PolyMAC_MPFA, equation().inconnue());
  const Domaine_PolyMAC_MPFA& domaine = ref_cast(Domaine_PolyMAC_MPFA, equation().domaine_dis());
  const IntTab& f_e = domaine.face_voisins(), &fcl = ch.fcl();
  const DoubleVect& pe = equation().milieu().porosite_elem(), &pf = equation().milieu().porosite_face(), &ve = domaine.volumes(), &vf = domaine.volumes_entrelaces(), &fs = domaine.face_surfaces();
  const DoubleTab& vf_dir = domaine.volumes_entrelaces_dir(), &n_f = domaine.face_normales();
  const DoubleTab& pvit = ch.passe(),
                   &alpha = pbm.equation_masse().inconnue().passe(),
                    &press = ref_cast(QDM_Multiphase, pbm.equation_qdm()).pression().passe(),
                     &temp  = pbm.equation_energie().inconnue().passe(),
                      &rho   = equation().milieu().masse_volumique().passe(),
                       &mu    = ref_cast(Fluide_base, equation().milieu()).viscosite_dynamique().passe(),
                        &y_elem = domaine.y_elem(),
                         &y_faces = domaine.y_faces(),
                          &n_y_elem = domaine.normale_paroi_elem(),
                           &n_y_faces = domaine.normale_paroi_faces(),
                            &d_bulles = equation().probleme().get_champ("diametre_bulles").valeurs(),
                             *k_turb = (equation().probleme().has_champ("k")) ? &equation().probleme().get_champ("k").passe() : nullptr,
                              * k_WIT = (equation().probleme().has_champ("k_WIT")) ? &equation().probleme().get_champ("k_WIT").passe() : nullptr ;
  const Milieu_composite& milc = ref_cast(Milieu_composite, equation().milieu());
 
  const int N = pvit.line_size();
  int Np = press.line_size();
  int Nk = (k_turb) ? (*k_turb).dimension(1) : 1;
  int D = dimension;
  int nf_tot = domaine.nb_faces_tot();
  const int nf = domaine.nb_faces();
  int ne_tot = domaine.nb_elem_tot();
  const int cR = (rho.dimension_tot(0) == 1);
  const int cM = (mu.dimension_tot(0) == 1);
 
  DoubleTrav nut(domaine.nb_elem_tot(), N); // turbulent viscosity
  if (is_turb)
    ref_cast(Viscosite_turbulente_base, ref_cast(Op_Diff_Turbulent_PolyMAC_MPFA_Face, equation().operateur(0).l_op_base()).correlation()).eddy_viscosity(nut); //remplissage par la correlation
 
  // Input-output
  const Dispersion_bulles_base& correlation_db = ref_cast(Dispersion_bulles_base, correlation_dispersion_.valeur());
  Dispersion_bulles_base::input_t in;
  Dispersion_bulles_base::output_t out;
  in.alpha.resize(N);
  in.T.resize(N);
  in.p.resize(N);
  in.rho.resize(N);
  in.mu.resize(N);
  in.sigma.resize(N*(N-1)/2);
  in.k_turb.resize(N);
  in.nut.resize(N);
  in.d_bulles.resize(N);
  in.nv.resize(N, N);
  out.Ctd.resize(N, N);
 
  // There is no need to calculate the gradient of alpha here
 
  // Et pour les methodes span de la classe Interface pour choper la tension de surface
  const int nb_max_sat =  N*(N - 1)/2;
  DoubleTrav Sigma_tab(ne_tot, nb_max_sat);
 
  // TODO: make a function from this k-loop
  // remplir les tabs ...
  for (int k = 0; k < N; k++)
    for (int l = k + 1; l < N; l++)
      {
        if (milc.has_saturation(k, l))
          {
            Saturation_base& z_sat = milc.get_saturation(k, l);
            const int ind_trav = sigma_pair_index(k, l, N);
            // recuperer sigma ...
            const DoubleTab& sig = z_sat.get_sigma_tab();
            // fill in the good case
            for (int ii = 0; ii < ne_tot; ii++)
              Sigma_tab(ii, ind_trav) = sig(ii);
          }
        else if (milc.has_interface(k, l))
          {
            Interface_base& sat = milc.get_interface(k, l);
            const int ind_trav = sigma_pair_index(k, l, N);
            for (int i = 0 ; i<ne_tot ; i++)
              Sigma_tab(i,ind_trav) = sat.sigma(temp(i,k),press(i,k * (Np > 1))) ;
          }
      }
 
  /* faces */
  for (int f = 0; f < nf; f++)
    if (fcl(f, 0) < 2)
      {
        in.alpha=0., in.T=0., in.p=0., in.rho=0., in.mu=0., in.sigma=0., in.k_turb=0., in.nut=0., in.d_bulles=0., in.nv=0.;
        int e {0};
        for (int c = 0; c < 2 && (e = f_e(f, c)) >= 0; c++)
          {
            for (int n = 0; n < N; n++)
              {
                in.alpha[n] += vf_dir(f, c)/vf(f) * alpha(e, n);
                in.p[n]     += vf_dir(f, c)/vf(f) * press(e, n * (Np > 1));
                in.T[n]     += vf_dir(f, c)/vf(f) * temp(e, n);
                in.rho[n]   += vf_dir(f, c)/vf(f) * rho(!cR * e, n);
                in.mu[n]    += vf_dir(f, c)/vf(f) * mu(!cM * e, n);
                in.nut[n]   += is_turb    ? vf_dir(f, c)/vf(f) * nut(e,n) : 0;
                in.d_bulles[n] += vf_dir(f, c)/vf(f) * d_bulles(e,n);
                for (int k = n + 1; k < N; k++)
                  if (milc.has_interface(n, k))
                    {
                      const int ind_trav = sigma_pair_index(n, k, N);
                      in.sigma[ind_trav] += vf_dir(f, c) / vf(f) * Sigma_tab(e, ind_trav);
                    }
                for (int k = 0; k < N; k++)
                  in.nv(k, n) += vf_dir(f, c)/vf(f) * ch.v_norm(pvit, pvit, e, f, k, n, nullptr, nullptr);
              }
            for (int n = 0; n <Nk; n++) in.k_turb[n]   += (k_turb)   ? vf_dir(f, c)/vf(f) * (*k_turb)(e,0) : 0;
            in.k_WIT   += (k_WIT)   ? vf_dir(f, c)/vf(f) * (*k_WIT)(e,0) : 0.;
            in.e = e;
          }
 
        correlation_db.coefficient(in, out);
 
        double sum_alphag_wall = 0 ;
        for (int k = 0; k<N ; k++)
          if (k!=n_l) sum_alphag_wall += (y_faces(f)<portee_disp_*in.d_bulles[k]/2.) ? in.alpha[k] * (portee_disp_*in.d_bulles[k]-2*y_faces(f))/(portee_disp_*in.d_bulles[k]-y_faces(f)) :0 ;
 
        for (int k = 0; k < N; k++)
          if (k != n_l)
            if (y_faces(f)<portee_disp_*in.d_bulles[k]/2.)
              {
                double fac = 0 ;
                for (int d = 0 ; d<D ; d++) fac += n_y_faces(f, d) * n_f(f, d)/fs(f);
 
                fac *= beta_disp_*pf(f) * vf(f) ;
                secmem(f, k)   += fac * out.Ctd(k, n_l) * 1/y_faces(f) * in.alpha[k] * (portee_disp_*in.d_bulles[k]-2*y_faces(f))/(portee_disp_*in.d_bulles[k]-y_faces(f));
                secmem(f, k)   += fac * out.Ctd(n_l, k) * 1/y_faces(f) * sum_alphag_wall;
                secmem(f, n_l) -= fac * out.Ctd(k, n_l) * 1/y_faces(f) * in.alpha[k] * (portee_disp_*in.d_bulles[k]-2*y_faces(f))/(portee_disp_*in.d_bulles[k]-y_faces(f));
                secmem(f, n_l) -= fac * out.Ctd(n_l, k) * 1/y_faces(f) * sum_alphag_wall;
              }
      }
 
  /* elements */
  for (int e = 0; e < ne_tot; e++)
    {
      /* arguments de coeff */
      for (int n = 0; n < N; n++)
        {
          in.alpha[n] = alpha(e, n);
          in.p[n]     = press(e, n * (Np > 1));
          in.T[n]     = temp(e, n);
          in.rho[n]   = rho(!cR * e, n);
          in.mu[n]    = mu(!cM * e, n);
          in.nut[n]   = is_turb    ? nut(e,n) : 0;
          in.d_bulles[n] = d_bulles(e,n) ;
          for (int k = n+1; k < N; k++)
            if (milc.has_interface(n,k))
              {
                const int ind_trav = sigma_pair_index(n, k, N);
                in.sigma[ind_trav] = Sigma_tab(e, ind_trav);
              }
          for (int k = 0; k < N; k++)
            in.nv(k, n) = ch.v_norm(pvit, pvit, e, -1, k, n, nullptr, nullptr);
        }
      for (int n = 0; n <Nk; n++) in.k_turb[n]   = (k_turb) ? (*k_turb)(e,0) : 0;
      in.k_WIT   = (k_WIT) ? (*k_WIT)(e,0) : 0;
      in.e = e;
 
      correlation_db.coefficient(in, out);
 
      double sum_alphag_wall = 0 ;
      for (int k = 0; k<N ; k++)
        if (k!=n_l) sum_alphag_wall += (y_elem(e)<portee_disp_*d_bulles(e,k)/2.) ? alpha(e,k) *(portee_disp_*d_bulles(e,k)-2*y_elem(e))/(portee_disp_*d_bulles(e,k)-y_elem(e)) :0 ;
      for (int d = 0, i = nf_tot + D * e; d < D; d++, i++)
        for (int k = 0; k < N; k++)
          if (k != n_l)
            if (y_elem(e)<portee_disp_*d_bulles(e,k)/2)
              {
                double fac = beta_disp_*pe(e) * ve(e);
 
                secmem(i, k)   += fac * out.Ctd(k, n_l) * 1/y_elem(e) * alpha(e,k) * (portee_disp_*d_bulles(e,k)-2*y_elem(e))/(portee_disp_*d_bulles(e,k)-y_elem(e)) * n_y_elem(e, d);
                secmem(i, k)   += fac * out.Ctd(n_l, k) * 1/y_elem(e) * sum_alphag_wall                                      * n_y_elem(e, d);
                secmem(i, n_l) -= fac * out.Ctd(k, n_l) * 1/y_elem(e) * alpha(e,k) * (portee_disp_*d_bulles(e,k)-2*y_elem(e))/(portee_disp_*d_bulles(e,k)-y_elem(e)) * n_y_elem(e, d);
                secmem(i, n_l) -= fac * out.Ctd(n_l, k) * 1/y_elem(e) * sum_alphag_wall                                      * n_y_elem(e, d);
              }
    }
}
 
 
void Correction_Lubchenko_PolyMAC_MPFA::ajouter_blocs_lift(matrices_t matrices, DoubleTab& secmem, const tabs_t& semi_impl ) const
{
  const Pb_Multiphase& pbm = ref_cast(Pb_Multiphase, equation().probleme());
  const Champ_Face_PolyMAC_MPFA& ch = ref_cast(Champ_Face_PolyMAC_MPFA, equation().inconnue());
  const Domaine_PolyMAC_MPFA& domaine = ref_cast(Domaine_PolyMAC_MPFA, equation().domaine_dis());
  const IntTab& f_e = domaine.face_voisins(), &fcl = ch.fcl(), &e_f = domaine.elem_faces();
  const DoubleVect& pe = equation().milieu().porosite_elem(), &pf = equation().milieu().porosite_face(), &ve = domaine.volumes(), &vf = domaine.volumes_entrelaces(), &fs = domaine.face_surfaces();
  const DoubleTab& vf_dir = domaine.volumes_entrelaces_dir(), &n_f = domaine.face_normales();
  const DoubleTab& pvit = ch.passe(),
                   &alpha = pbm.equation_masse().inconnue().passe(),
                    &press = ref_cast(QDM_Multiphase, pbm.equation_qdm()).pression().passe(),
                     &temp  = pbm.equation_energie().inconnue().passe(),
                      &rho   = equation().milieu().masse_volumique().passe(),
                       &mu    = ref_cast(Fluide_base, equation().milieu()).viscosite_dynamique().passe(),
                        &vort  = equation().probleme().get_champ("vorticite").valeurs(),
                         &y_elem = domaine.y_elem(),
                          &y_faces = domaine.y_faces(),
                           &d_bulles = equation().probleme().get_champ("diametre_bulles").valeurs(),
                            &grad_v = equation().probleme().get_champ("gradient_vitesse").valeurs(),
                             * k_turb = (equation().probleme().has_champ("k")) ? &equation().probleme().get_champ("k").passe() : nullptr ;
 
  const Milieu_composite& milc = ref_cast(Milieu_composite, equation().milieu());
 
  int N = pvit.line_size() , Np = press.line_size(), Nk = (k_turb) ? (*k_turb).dimension(1) : 1, D = dimension,
      nf_tot = domaine.nb_faces_tot(), cR = (rho.dimension_tot(0) == 1), cM = (mu.dimension_tot(0) == 1);
 
  DoubleTrav vr_l(N,D), scal_ur(N), scal_u(N), pvit_l(N, D), vort_l( D==2 ? 1 :D), grad_l(D,D), scal_grad(D); // Requis pour corrections vort et u_l-u-g
 
  const Portance_interfaciale_base& correlation_pi = ref_cast(Portance_interfaciale_base, correlation_lift_.valeur());
  double vl_norm ;
 
  Portance_interfaciale_base::input_t in;
  Portance_interfaciale_base::output_t out;
  in.alpha.resize(N), in.T.resize(N), in.p.resize(N), in.rho.resize(N), in.mu.resize(N), in.sigma.resize(N*(N-1)/2), in.k_turb.resize(N), in.d_bulles.resize(N), in.nv.resize(N, N);
  out.Cl.resize(N, N);
 
  // Et pour les methodes span de la classe Interface pour choper la tension de surface
  const int ne_tot = domaine.nb_elem_tot(), nb_max_sat =  N * (N-1) /2; // oui !! suite arithmetique !!
  DoubleTrav Sigma_tab(ne_tot,nb_max_sat);
 
  // remplir les tabs ...
  for (int k = 0; k < N; k++)
    for (int l = k + 1; l < N; l++)
      {
        if (milc.has_saturation(k, l))
          {
            Saturation_base& z_sat = milc.get_saturation(k, l);
            const int ind_trav = sigma_pair_index(k, l, N);
            // XXX XXX XXX
            // Attention c'est dangereux ! on suppose pour le moment que le champ de pression a 1 comp. Par contre la taille de res est nb_max_sat*nbelem !!
            // Aussi, on passe le Span le nbelem pour le champ de pression et pas nbelem_tot ....
            assert(press.line_size() == 1);
            assert(temp.line_size() == N);
            z_sat.get_sigma(temp.get_span_tot(), press.get_span_tot(), Sigma_tab.get_span_tot(), nb_max_sat, ind_trav);
          }
        else if (milc.has_interface(k, l))
          {
            Interface_base& sat = milc.get_interface(k,l);
            const int ind_trav = sigma_pair_index(k, l, N);
            for (int i = 0 ; i<ne_tot ; i++) Sigma_tab(i,ind_trav) = sat.sigma(temp(i,k),press(i,k * (Np > 1))) ;
          }
      }
 
  /* elements */
  int f;
  for (int e = 0; e < ne_tot; e++)
    {
      /* arguments de coeff */
      for (int n=0; n<N; n++)
        {
          in.alpha[n] = alpha(e, n);
          in.p[n]     = press(e, n * (Np > 1));
          in.T[n]     = temp(e, n);
          in.rho[n]   = rho(!cR * e, n);
          in.mu[n]    = mu(!cM * e, n);
          in.d_bulles[n] = d_bulles(e,n) ;
          for (int k = n+1; k < N; k++)
            if (milc.has_interface(n,k))
              {
                const int ind_trav = sigma_pair_index(n, k, N);
                in.sigma[ind_trav] = Sigma_tab(e, ind_trav);
              }
          for (int k = 0; k < N; k++)
            in.nv(k, n) = ch.v_norm(pvit, pvit, e, -1, k, n, nullptr, nullptr);
        }
      for (int n = 0; n <Nk; n++) in.k_turb[n]   = (k_turb) ? (*k_turb)(e,0) : 0;
 
      correlation_pi.coefficient(in, out);
 
      double fac_e = beta_lift_*pe(e) * ve(e);
      int i = nf_tot + D * e;
 
      // Experimentation sur la portance
      vl_norm = 0;
      scal_ur = 0 ;
      for (int d = 0 ; d < D ; d++) vl_norm += pvit(i+d, n_l)*pvit(i+d, n_l);
      vl_norm = std::sqrt(vl_norm);
      if (vl_norm > 1.e-6)
        {
          for (int k = 0; k < N; k++)
            for (int d = 0 ; d < D ; d++) scal_ur(k) += pvit(i+d, n_l)/vl_norm * (pvit(i+d, k) -pvit(i+d, n_l));
          for (int k = 0; k < N; k++)
            for (int d = 0 ; d < D ; d++) vr_l(k, d)  = pvit(i+d, n_l)/vl_norm * scal_ur(k) ;
        }
      else for (int k=0 ; k<N ; k++)
          for (int d=0 ; d<D ; d++) vr_l(k, d) = pvit(i+d, k) -pvit(i+d, n_l) ;
 
      if (D==2)
        {
          for (int k = 0; k < N; k++)
            if (k!= n_l) // gas phase
              {
                // Damping of the lift force close to the wall;
                if      (y_elem(e) < .5*d_bulles(e,k)*portee_lift_) fac_e *= -1 ; // suppresses lift
                else if (y_elem(e) >    d_bulles(e,k)*portee_lift_) fac_e *=  0 ; // no effect
                else   fac_e *= (3*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 2) - 2*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 3)) - 1; // partial damping
 
                secmem(i, n_l) += fac_e * out.Cl(n_l, k) * vr_l(k, 1) * vort(e, 0) ;
                secmem(i,  k ) -= fac_e * out.Cl(n_l, k) * vr_l(k, 1) * vort(e, 0) ;
                secmem(i+1,n_l)-= fac_e * out.Cl(n_l, k) * vr_l(k, 0) * vort(e, 0) ;
                secmem(i+1, k )+= fac_e * out.Cl(n_l, k) * vr_l(k, 0) * vort(e, 0) ;
              } // 100% explicit
          for (int b = 0; b < e_f.dimension(1) && (f = e_f(e, b)) >= 0; b++)
            if (f<domaine.nb_faces())
              if (fcl(f, 0) < 2)
                for (int k = 0; k < N; k++)
                  if (k!= n_l) // gas phase
                    {
                      int c = (e == f_e(f, 0)) ? 0 : 1 ;
                      double fac_f = beta_lift_*pf(f) * vf_dir(f, c);  // Coherence with portance_interfaciale that calculates the correlation at the element
 
                      if   (y_elem(e) < .5*d_bulles(e,k)*portee_lift_) fac_f *= -1 ; // suppresses lift
                      else if (y_elem(e) > d_bulles(e,k)*portee_lift_) fac_f *=  0 ; // no effect
                      else fac_f *= (3*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 2) - 2*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 3)) - 1; // partial damping
 
                      secmem(f, n_l) += fac_f * n_f(f, 0)/fs(f) * out.Cl(n_l, k) * vr_l(k, 1) * vort(e, 0) ;
                      secmem(f,  k ) -= fac_f * n_f(f, 0)/fs(f) * out.Cl(n_l, k) * vr_l(k, 1) * vort(e, 0) ;
                      secmem(f, n_l) -= fac_f * n_f(f, 1)/fs(f) * out.Cl(n_l, k) * vr_l(k, 0) * vort(e, 0) ;
                      secmem(f,  k ) += fac_f * n_f(f, 1)/fs(f) * out.Cl(n_l, k) * vr_l(k, 0) * vort(e, 0) ;
                    } // 100% explicit
 
        }
 
      if (D==3)
        {
          for (int k = 0; k < N; k++)
            if (k!= n_l) // gas phase
              {
                // Damping of the lift force close to the wall;
                if (y_elem(e) < .5*d_bulles(e,k)*portee_lift_) fac_e *= -1 ; // suppresses lift
                else if (y_elem(e) >    d_bulles(e,k)*portee_lift_) fac_e *=  0 ; // no effect
                else fac_e *= (3*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 2) - 2*std::pow(2*y_elem(e)/(d_bulles(e,k)*portee_lift_)-1, 3)) - 1; // partial damping
 
                secmem(i, n_l) += fac_e * out.Cl(n_l, k) * (vr_l(k, 1) * vort(e, 2*N+n_l) - vr_l(k, 2) * vort(e, 1*N+n_l)) ;
                secmem(i,  k ) -= fac_e * out.Cl(n_l, k) * (vr_l(k, 1) * vort(e, 2*N+n_l) - vr_l(k, 2) * vort(e, 1*N+n_l)) ;
                secmem(i+1,n_l)+= fac_e * out.Cl(n_l, k) * (vr_l(k, 2) * vort(e, 0*N+n_l) - vr_l(k, 0) * vort(e, 2*N+n_l)) ;
                secmem(i+1, k )-= fac_e * out.Cl(n_l, k) * (vr_l(k, 2) * vort(e, 0*N+n_l) - vr_l(k, 0) * vort(e, 2*N+n_l)) ;
                secmem(i+2,n_l)+= fac_e * out.Cl(n_l, k) * (vr_l(k, 0) * vort(e, 1*N+n_l) - vr_l(k, 1) * vort(e, 0*N+n_l)) ;
                secmem(i+2, k )-= fac_e * out.Cl(n_l, k) * (vr_l(k, 0) * vort(e, 1*N+n_l) - vr_l(k, 1) * vort(e, 0*N+n_l)) ;
              } // 100% explicit
        }
 
    }
 
  int c, e, n, k, d, d2;
  double fac_f ;
 
  if (D==3)
    for (f = 0 ; f<domaine.nb_faces() ; f++)
      if (fcl(f, 0) < 2)
        {
          in.alpha=0., in.T=0., in.p=0., in.rho=0., in.mu=0., in.sigma=0., in.k_turb=0., in.d_bulles=0., in.nv=0.;
          for ( c = 0; c < 2 && (e = f_e(f, c)) >= 0; c++)
            {
              for (n = 0; n < N; n++)
                {
                  in.alpha[n] += vf_dir(f, c)/vf(f) * alpha(e, n);
                  in.p[n]     += vf_dir(f, c)/vf(f) * press(e, n * (Np > 1));
                  in.T[n]     += vf_dir(f, c)/vf(f) * temp(e, n);
                  in.rho[n]   += vf_dir(f, c)/vf(f) * rho(!cR * e, n);
                  in.mu[n]    += vf_dir(f, c)/vf(f) * mu(!cM * e, n);
                  in.d_bulles[n] += vf_dir(f, c)/vf(f) *d_bulles(e,n) ;
                  for (k = n+1; k < N; k++)
                    if (milc.has_interface(n,k))
                      {
                        const int ind_trav = sigma_pair_index(n, k, N);
                        in.sigma[ind_trav] += vf_dir(f, c) / vf(f) * Sigma_tab(e, ind_trav);
                      }
                  for (k = 0; k < N; k++)
                    in.nv(k, n) += vf_dir(f, c)/vf(f) * ch.v_norm(pvit, pvit, e, f, k, n, nullptr, nullptr);
                }
              for (n = 0; n <Nk; n++) in.k_turb[n]   += (k_turb)   ? vf_dir(f, c)/vf(f) * (*k_turb)(e,0) : 0;
            }
 
          correlation_pi.coefficient(in, out);
 
          grad_l = 0; // we fill grad_l so that grad_l(d, d2) = du_d/dx_d2 by averaging between both elements
          for (d = 0 ; d<D ; d++)
            for (d2 = 0 ; d2<D ; d2++)
              for (c=0 ; c<2  && (e = f_e(f, c)) >= 0; c++)
                grad_l(d, d2) += vf_dir(f, c)/vf(f)*grad_v(nf_tot + D*e + d2 , n_l * D + d) ;
          //We replace the n_l components by the one calculated without interpolation to elements
          scal_grad = 0 ; // scal_grad(d) = grad(u_d).n_f
          for (d = 0 ; d<D ; d++)
            for (d2 = 0 ; d2<D ; d2++)
              scal_grad(d) += grad_l(d, d2)*n_f(f, d2)/fs(f);
          for (d = 0 ; d<D ; d++)
            for (d2 = 0 ; d2<D ; d2++)
              grad_l(d, d2) += (grad_v(f ,n_l*D+d) - scal_grad(d)) * n_f(f, d2)/fs(f);
          // We calculate the local vorticity using this local gradient
          vort_l(0) = grad_l(2, 1) - grad_l(1, 2); // dUz/dy - dUy/dz
          vort_l(1) = grad_l(0, 2) - grad_l(2, 0); // dUx/dz - dUz/dx
          vort_l(2) = grad_l(1, 0) - grad_l(0, 1); // dUy/dx - dUx/dy
 
          // We also need to calculate relative velocity at the face
          pvit_l = 0 ;
          for (d = 0 ; d<D ; d++)
            for (k = 0 ; k<N ; k++)
              for (c=0 ; c<2 && (e = f_e(f, c)) >= 0; c++)
                pvit_l(k, d) += vf_dir(f, c)/vf(f)*pvit(domaine.nb_faces_tot()+D*e+d, k) ;
          scal_u = 0;
          for (k = 0 ; k<N ; k++)
            for (d = 0 ; d<D ; d++)
              scal_u(k) += pvit_l(k, d)*n_f(f, d)/fs(f);
          for (k = 0 ; k<N ; k++)
            for (d = 0 ; d<D ; d++)
              pvit_l(k, d) += (pvit(f, k) - scal_u(k)) * n_f(f, d)/fs(f) ; // Corect velocity at the face
          vl_norm = 0;
          scal_ur = 0;
          for (d = 0 ; d < D ; d++) vl_norm += pvit_l(n_l, d)*pvit_l(n_l, d);
          vl_norm = std::sqrt(vl_norm);
          if (vl_norm > 1.e-6)
            {
              for (k = 0; k < N; k++)
                for (d = 0 ; d < D ; d++) scal_ur(k) += pvit_l(n_l, d)/vl_norm * (pvit_l(k, d) -pvit_l(n_l, d));
              for (k = 0; k < N; k++)
                for (d = 0 ; d < D ; d++) vr_l(k, d)  = pvit_l(n_l, d)/vl_norm * scal_ur(k) ;
            }
          else for (k=0 ; k<N ; k++)
              for (d=0 ; d<D ; d++) vr_l(k, d) = pvit_l(k, d)-pvit_l(n_l, d) ;
 
 
          // Use local vairables for the calculation of secmem
 
          for (k = 0; k < N; k++)
            if (k!= n_l) // gas phase
              {
                fac_f = beta_lift_*pf(f) * vf(f);
 
                if   (y_faces(f) < .5*in.d_bulles(k)*portee_lift_) fac_f *= -1 ; // suppresses lift
                else if (y_faces(f) > in.d_bulles(k)*portee_lift_) fac_f *=  0 ; // no effect
                else  fac_f *= (3*std::pow(2*y_faces(f)/(in.d_bulles(k)*portee_lift_)-1, 2) - 2*std::pow(2*y_faces(f)/(in.d_bulles(k)*portee_lift_)-1, 3)) - 1; // partial damping
 
                secmem(f, n_l) += fac_f * n_f(f, 0)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 1) * vort_l(2) - vr_l(k, 2) * vort_l(1)) ;
                secmem(f,  k ) -= fac_f * n_f(f, 0)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 1) * vort_l(2) - vr_l(k, 2) * vort_l(1)) ;
                secmem(f, n_l) += fac_f * n_f(f, 1)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 2) * vort_l(0) - vr_l(k, 0) * vort_l(2)) ;
                secmem(f,  k ) -= fac_f * n_f(f, 1)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 2) * vort_l(0) - vr_l(k, 0) * vort_l(2)) ;
                secmem(f, n_l) += fac_f * n_f(f, 2)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 0) * vort_l(1) - vr_l(k, 1) * vort_l(0)) ;
                secmem(f,  k ) -= fac_f * n_f(f, 2)/fs(f) * out.Cl(n_l, k) * (vr_l(k, 0) * vort_l(1) - vr_l(k, 1) * vort_l(0)) ;
              } // 100% explicit
        }
 
 
}
 
 
void Correction_Lubchenko_PolyMAC_MPFA::ajouter_blocs_BIF(matrices_t matrices, DoubleTab& secmem, const tabs_t& semi_impl ) const
{
  const Domaine_PolyMAC_MPFA&                      domaine = ref_cast(Domaine_PolyMAC_MPFA, equation().domaine_dis());
  const Probleme_base&                       pb = ref_cast(Probleme_base, equation().probleme());
  const Navier_Stokes_std&               eq_qdm = ref_cast(Navier_Stokes_std, pb.equation(0));
  const Op_Diff_Turbulent_PolyMAC_MPFA_Face& Op_diff = ref_cast(Op_Diff_Turbulent_PolyMAC_MPFA_Face, eq_qdm.operateur(0).l_op_base());
  const DoubleTab&                      tab_rho = equation().probleme().get_champ("masse_volumique").passe();
  const DoubleTab&                      tab_alp = equation().probleme().get_champ("alpha").passe();
  const DoubleTab& d_bulles = equation().probleme().get_champ("diametre_bulles").valeurs();
  const DoubleTab& y_elem = domaine.y_elem(),
                   &y_faces = domaine.y_faces();
 
  const DoubleTab&                       vf_dir = domaine.volumes_entrelaces_dir(), &xp = domaine.xp(), &xv = domaine.xv();
  const DoubleVect& pe = equation().milieu().porosite_elem(), &ve = domaine.volumes(), &fs = domaine.face_surfaces(), &vf = domaine.volumes_entrelaces();
  const DoubleTab& normales_f = domaine.face_normales();
  const IntTab& voisins_f = domaine.face_voisins(), &e_f = domaine.elem_faces(), &f_e = domaine.face_voisins();
 
  const Viscosite_turbulente_multiple&    visc_turb = ref_cast(Viscosite_turbulente_multiple, Op_diff.correlation());
 
  int N = pb.get_champ("vitesse").valeurs().dimension(1), D = dimension, nf_tot = domaine.nb_faces_tot(), nf = domaine.nb_faces(), ne_tot = domaine.nb_elem_tot() ;
 
  // On recupere les tensions de reynolds des termes de BIF
  DoubleTrav Rij(0, N, D, D);
  MD_Vector_tools::creer_tableau_distribue(eq_qdm.pression().valeurs().get_md_vector(), Rij); //Necessary to compare size in reynolds_stress()
  visc_turb.reynolds_stress_BIF(Rij);
 
  DoubleTrav grad_Rij(0, N, D, D);
  MD_Vector_tools::creer_tableau_distribue(eq_qdm.vitesse().valeurs().get_md_vector(), grad_Rij); //Necessary to exchange virtual elements after calculation of the gradient at the faces()
 
  const Champ_Elem_PolyMAC_MPFA& ch_alpha = ref_cast(Champ_Elem_PolyMAC_MPFA, equation().probleme().get_champ("alpha"));    // Champ alpha qui servira à obtenir les coeffs du gradient ; normalement toujours des CAL de Neumann ; terme source qui n'apparait qu'en multiphase
  ch_alpha.init_grad(0); // Initialisation des tables fgrad_d, fgrad_e, fgrad_w qui dependent de la discretisation et du type de conditions aux limites --> pas de mises a jour necessaires
  IntTab& fg_d = ch_alpha.fgrad_d, fg_e = ch_alpha.fgrad_e; // Tables utilisees dans domaine_PolyMAC_MPFA::fgrad pour le calcul du gradient
  DoubleTab fg_w = ch_alpha.fgrad_w;
 
  // On calcule le gradient de Rij aux faces
  for (int n = 0; n < N; n++)
    for (int f = 0; f < nf_tot; f++)
      for (int d_i = 0; d_i <D ; d_i++)
        for (int d_j = 0; d_j <D ; d_j++)
          {
            grad_Rij(f, n, d_i, d_j) = 0;
            // grad_Rij(face, phase, x-coord, y-coord)   or
            // grad_Rij(nb_face_tot + dimension*element*gradient_component, phase, x-coord, y-coord)
            for (int j = fg_d(f); j < fg_d(f+1) ; j++)
              {
                int e = fg_e(j);
                int f_bord;
                if ( (f_bord = e - ne_tot) < 0) //contribution d'un element
                  grad_Rij(f, n, d_i, d_j) += fg_w(j) * Rij(e, n, d_i, d_j);
                else if ( (ch_alpha.fcl()(f_bord, 0) == 1) || (ch_alpha.fcl()(f_bord, 0) == 2)
                          || (ch_alpha.fcl()(f_bord, 0) == 3) || (ch_alpha.fcl()(f_bord, 0) == 6))
                  {
                    Process::exit("You must have a neumann limit condition on alpha for RIJ_BIF to work !");
                  }
              }
          }
 
  // On interpole le gradient de Rij aux elements
  for (int n = 0; n < N; n++)
    for (int e = 0; e < ne_tot; e++)
      for (int d_d=0 ; d_d<D ; d_d++) // on derive / d_d
        for (int d_i = 0; d_i <D ; d_i++)
          for (int d_j = 0; d_j <D ; d_j++)
            {
              grad_Rij(nf_tot + D *e + d_d, n, d_i,  d_j) = 0;
              for (int j = 0, f; j < e_f.dimension(1) && (f = e_f(e, j)) >= 0; j++)
                grad_Rij(nf_tot + D *e + d_d, n, d_i,  d_j) += (e == f_e(f, 0) ? 1 : -1) * fs(f) * (xv(f, d_d) - xp(e, d_d)) / ve(e) * grad_Rij(f, n, d_i,  d_j);
            }
 
  // On calcule le second membre aux elements
 
  for(int e = 0 ; e < ne_tot ; e++)
    for(int n = 0; n<N ; n++)
      for (int d_i = 0; d_i < D; d_i++)
        {
          // Find max value of d_bulles
          double d_b_elem = 0;
          for(int k = 0; k<N ; k++)
            {
              if (k!=n_l && d_bulles(e,k)>d_b_elem) d_b_elem = d_bulles(e,k);
            }
          // BIF correction in the near wall region
          if (y_elem(e) < 0.5 * d_b_elem)
            {
              double secmem_en = 0;
              for (int d_j = 0; d_j < D; d_j++)
                secmem_en -= grad_Rij(nf_tot + D *e + d_j, n, d_i,  d_j) ; // On annule la contribution de BIF sur la qdm lorsque la distance à la paroi y<0.5*d_bulles
              secmem_en *= (-1) * pe(e) * ve(e) * tab_alp(e, n) * tab_rho(e, n) ; // For us, Rij = < u_i u_j >, therefore *(-1)
              secmem(nf_tot + e*D + d_i, n) += secmem_en;
            }
        }
 
 
  // On calcule le second membre aux faces
 
  int e;
 
  for(int f = 0 ; f < nf ; f++)
    for(int n = 0; n<N ; n++)
      for (int i = 0; i < 2 && (e = voisins_f(f, i)) >= 0; i++)
        {
          // Find max value of d_bulles
          double d_b_face = 0;
          for(int k = 0; k<N ; k++)
            {
              if (k!=n_l && d_bulles(e,k)>d_b_face) d_b_face = d_bulles(e,k);
            }
          // BIF correction in the near wall region
          double d_b = vf_dir(f, i)/vf(f) * d_b_face ;
          if (y_faces(f) < 0.5 * d_b)
            {
              DoubleTrav secmem_en(3); // Contains the vector of the divergence of R_ij at the face
              secmem_en = 0;
              for (int d_i = 0; d_i < D; d_i++)
                for (int d_j = 0; d_j < D; d_j++)
                  {
                    secmem_en(d_i) -= grad_Rij(nf_tot + D *e + d_j, n, d_i,  d_j) ;
                  }
 
              for (int d_i = 0; d_i < D; d_i++)
                secmem_en(d_i) *= (-1) * pe(e) * vf_dir(f, i) * tab_alp(e, n) * tab_rho(e, n);// For us, Rij = < u_i u_j >, therefore *(-1)
              double flux_face = domaine.dot(&normales_f(f, 0), &secmem_en(0));
              secmem(f, n) += flux_face;
            }
 
        }
 
}