FiniteVolumesDiffusion.hpp

#ifndef FINITE_VOLUMES_DIFFUSION_HPP
#define FINITE_VOLUMES_DIFFUSION_HPP

// --- INCLUSION fichiers headers ---

#include <Kokkos_Core.hpp>

#include <rang.hpp>
#include <BlockPerfectGas.hpp>

#include <TinyVector.hpp>
#include <TinyMatrix.hpp>
#include <Mesh.hpp>
#include <MeshData.hpp>
#include <FiniteVolumesEulerUnknowns.hpp>

// ---------------------------------

// Creation classe FiniteVolumesDiffusion 

template<typename MeshData> 
class FiniteVolumesDiffusion 
{
  typedef typename MeshData::MeshType MeshType; 
  typedef FiniteVolumesEulerUnknowns<MeshData> UnknownsType; 

  MeshData& m_mesh_data; 
  const MeshType& m_mesh; 
  const typename MeshType::Connectivity& m_connectivity; 

  constexpr static size_t dimension = MeshType::dimension;

  typedef TinyVector<dimension> Rd; 
  typedef TinyMatrix<dimension> Rdd; 

private:

 // Sert a calculer les reductions (en gros calculer le min sur des
 // vecteurs en parallele)
  struct ReduceMin
  {
  private:
    const Kokkos::View<const double*> x_;

  public:
    typedef Kokkos::View<const double*>::non_const_value_type value_type;

    ReduceMin(const Kokkos::View<const double*>& x) : x_ (x) {}

    typedef Kokkos::View<const double*>::size_type size_type;
    
    KOKKOS_INLINE_FUNCTION void
    operator() (const size_type i, value_type& update) const
    {
      if (x_(i) < update) {
	update = x_(i);
      }
    }

    KOKKOS_INLINE_FUNCTION void
    join (volatile value_type& dst,
	  const volatile value_type& src) const
    {
      if (src < dst) {
	dst = src;
      }
    }

    KOKKOS_INLINE_FUNCTION void
    init (value_type& dst) const
    { // The identity under max is -Inf.
      dst= Kokkos::reduction_identity<value_type>::min();
    }
  };

  // Calcule un Fl
  Kokkos::View<Rdd*> 
  computeFl(const Kokkos::View<const Rd**>& Cjr,
	    const Kokkos::View<const Rd*>& uj,
	    const Kokkos::View<const double*>& kj,
	    const Kokkos::View<const Rd*>& uL,
	    const Kokkos::View<const Rd*>& uR,
	    const Kokkos::View<const double*>& kL,
	    const Kokkos::View<const double*>& kR,
	    const double& t) {

    const Kokkos::View<const unsigned int**>& face_cells = m_connectivity.faceCells();

    const Kokkos::View<const unsigned short*> face_nb_cells
      = m_connectivity.faceNbCells();

    const Kokkos::View<const unsigned short**> face_cell_local_face
      = m_mesh.connectivity().faceCellLocalFace();

    const Kokkos::View<const double*>& Vl = m_mesh_data.Vl();
    const Kokkos::View<const double*>& Vj = m_mesh_data.Vj();
    const Kokkos::View<const Rd*> xr = m_mesh.xr();

    Kokkos::parallel_for(m_mesh.numberOfFaces(), KOKKOS_LAMBDA(const int& l) {
        Rdd sum = zero;
	double sum2 = 0.;
	double sum3 = 0.;
	for (int j=0; j<face_nb_cells(l); ++j) {
	    int cell_here = face_cells(l,j);
	    int local_face_number_in_cell = face_cell_local_face(l,j);
	    sum -= tensorProduct(uj(cell_here), Cjr(cell_here, local_face_number_in_cell));
	    sum2 += (1./Vj(cell_here))*kj(cell_here);
	    sum3 += 1./Vj(cell_here);
	}

	m_Fl(l) = ((sum2/sum3)/Vl(l))*sum;
	
      });

    // Conditions aux bords
    /*
    int cell_here = face_cells(0,0);
    int local_face_number_in_cell = face_cell_local_face(0,0);
    m_Fl(0) = -(kL(0) + kj(cell_here))*(1./(2*Vl(0)))*(tensorProduct(uj(cell_here), Cjr(cell_here, local_face_number_in_cell)) - tensorProduct(uL(0), Cjr(cell_here, local_face_number_in_cell)));
    //m_Fl(0) = -xr[0][0]*(tensorProduct(uj(cell_here), Cjr(cell_here, local_face_number_in_cell)) - tensorProduct(uL(0), Cjr(cell_here, local_face_number_in_cell)));
    cell_here = face_cells(m_mesh.numberOfFaces()-1,0);
    local_face_number_in_cell = face_cell_local_face(m_mesh.numberOfFaces()-1,0);
    m_Fl(m_mesh.numberOfFaces()-1) = -(kR(0) + kj(cell_here))*(1/(2.*Vl(m_mesh.numberOfFaces()-1)))*(tensorProduct(uj(cell_here), Cjr(cell_here, local_face_number_in_cell)) - tensorProduct(uR(0), Cjr(cell_here, local_face_number_in_cell)));
    //m_Fl(m_mesh.numberOfFaces()-1) = -xr[m_mesh.numberOfNodes()-1][0]*(tensorProduct(uj(cell_here), Cjr(cell_here, local_face_number_in_cell)) - tensorProduct(uR(0), Cjr(cell_here, local_face_number_in_cell)));
    */

    // k = 0.5
    //m_Fl(0,0) = -(t/((50./9.)-t*t))*0.5;
    //m_Fl(m_mesh.numberOfFaces()-1,0) = -(t/((50./9.)-t*t))*0.5;

    // k = x
    m_Fl(0,0) = -(t/((50./9.)-t*t))*xr[0][0];
    m_Fl(m_mesh.numberOfFaces()-1,0) = -(t/((50./9.)-t*t))*xr[m_mesh.numberOfFaces()-1][0];
    
    return m_Fl ;
  }

  // Calcule un Gl
  Kokkos::View<Rd*>  
  computeGl(const Kokkos::View<const Rd*>& uj,
	    const Kokkos::View<const Rdd*>& Fl,
	    const Kokkos::View<const Rd*>& uL,
	    const Kokkos::View<const Rd*>& uR,
	    const double& t) {

    const Kokkos::View<const unsigned int**>& face_cells = m_connectivity.faceCells();

    const Kokkos::View<const unsigned short*> face_nb_cells
      = m_connectivity.faceNbCells();

    const Kokkos::View<const unsigned short**> face_cell_local_face
      = m_mesh.connectivity().faceCellLocalFace();

    const Kokkos::View<const double*>& Vj = m_mesh_data.Vj();

    const Kokkos::View<const Rd*> xr = m_mesh.xr();

    Kokkos::parallel_for(m_mesh.numberOfFaces(), KOKKOS_LAMBDA(const int& l) {
        Rd sum = zero;
	double sum2 = 0.;
	for (int j=0; j<face_nb_cells(l); ++j) {
	  int cell_here = face_cells(l,j);
	  sum += (1./Vj(cell_here))*uj(cell_here);
	  sum2 += 1./Vj(cell_here);
	}                
	
	m_Gl(l) = (1./sum2)*Fl(l)*sum;
      });

    // Conditions aux bords
    // m_Gl(0) = Fl(0)*uL(0);
    //m_Gl(m_mesh.numberOfFaces()-1) = Fl(m_mesh.numberOfFaces()-1)*uR(0);

    m_Gl(0) = -(t/((50./9.)-t*t))*Fl(0,0)*xr(0);
    m_Gl(m_mesh.numberOfFaces()-1) = -(t/((50./9.)-t*t))*Fl(m_mesh.numberOfFaces()-1,0)*xr(m_mesh.numberOfFaces()-1);
    
    return m_Gl ;

  }

  // Calcule la liste des inverse d'une liste de matrices 
  // (pour l'instant, juste 1x1)
  void inverse(const Kokkos::View<const Rdd*>& A,
	       Kokkos::View<Rdd*>& inv_A) const {
    Kokkos::parallel_for(A.size(), KOKKOS_LAMBDA(const int& r) {
	inv_A(r) = Rdd{1./(A(r)(0,0))};
      });
  }

  // Calcule la liste des inverses d'une liste de reels
  void inverse(const Kokkos::View<const double*>& x,
	       Kokkos::View<double*>& inv_x) const {
    Kokkos::parallel_for(x.size(), KOKKOS_LAMBDA(const int& r) {
	inv_x(r) = 1./x(r);
      });
  }


  // Enchaine les operations pour calculer les flux (Fjr et Gjr) pour
  // pouvoir derouler le schema
  KOKKOS_INLINE_FUNCTION
  void computeExplicitFluxes(const Kokkos::View<const Rd*>& uj,
			     const Kokkos::View<const Rd**>& Cjr,
			     const Kokkos::View<const double*>& kj,
			     const Kokkos::View<const Rd*>& uL,
			     const Kokkos::View<const Rd*>& uR,
			     const Kokkos::View<const double*>& kL,
			     const Kokkos::View<const double*>& kR,
			     const double& t) { 
    Kokkos::View<Rdd*> Fl  = m_Fl ; 
    Fl  = computeFl (Cjr, uj, kj, uL, uR, kL, kR, t);
    Kokkos::View<Rd*> Gl  = m_Gl ; 
    Gl  = computeGl (uj, Fl, uL, uR, t);
  }

  Kokkos::View<Rdd*> m_Fl;
  Kokkos::View<Rd*> m_Gl;

public:
  FiniteVolumesDiffusion(MeshData& mesh_data,
			 UnknownsType& unknowns)
    : m_mesh_data(mesh_data),
      m_mesh(mesh_data.mesh()),
      m_connectivity(m_mesh.connectivity()),
      m_Fl("Fl", m_mesh.numberOfFaces()), 
      m_Gl("Gl", m_mesh.numberOfFaces())
  {
    ;
  }

  // Calcule une evaluation du pas de temps verifiant le CFL parabolique
  // Utilise la reduction definie dans la structure ReduceMin.
  KOKKOS_INLINE_FUNCTION
  double diffusion_dt(const Kokkos::View<const double*>& rhoj,
		      const Kokkos::View<const double*>& kj) const {

    Kokkos::View<double*> dt_j("dt_j", m_mesh.numberOfCells());

    const Kokkos::View<const Rd**> Cjr = m_mesh_data.Cjr();

    const Kokkos::View<const double*>& Vl = m_mesh_data.Vl();

    const Kokkos::View<const double*>& Vj = m_mesh_data.Vj();

    const Kokkos::View<const unsigned int**>& cell_faces = m_connectivity.cellFaces();

    const Kokkos::View<const unsigned short*> cell_nb_faces
      = m_connectivity.cellNbFaces();

    const Kokkos::View<const unsigned int**>& cell_nodes = m_connectivity.cellNodes();

    const Kokkos::View<const unsigned short*> cell_nb_nodes
      = m_connectivity.cellNbNodes();

    Kokkos::parallel_for(m_mesh.numberOfCells(), KOKKOS_LAMBDA(const int& j){
	double minVl = std::numeric_limits<double>::max();
	for (int ll=0; ll<cell_nb_faces(j); ++ll) {
	  minVl = std::min(minVl, Vl(cell_faces(j, ll)));
	}
	
	double sum = 0.;
	
	for (int m = 0; m < cell_nb_nodes(j); ++m) {
	 sum += kj(cell_nodes(j,m));
	}

	// dt_j[j]= 0.5*rhoj(j)*Vj(j)*(1./(2.*kj(j) + sum))*minVl;
	dt_j[j]= 0.5*rhoj(j)*Vj(j)*(1./sum)*minVl;
	
      });
    
    double dt = std::numeric_limits<double>::max();
    Kokkos::parallel_reduce(m_mesh.numberOfCells(), ReduceMin(dt_j), dt);

    return dt;
  }

  // Avance la valeur des inconnues pendant un pas de temps dt 
  void computeNextStep(const double& t, const double& dt,
		       UnknownsType& unknowns)
  {
    Kokkos::View<double*> rhoj = unknowns.rhoj();
    Kokkos::View<Rd*> uj = unknowns.uj();
    Kokkos::View<Rd*> Sj = unknowns.Sj();
    Kokkos::View<double*> Ej = unknowns.Ej();

    Kokkos::View<double*> ej = unknowns.ej();
    Kokkos::View<double*> gammaj = unknowns.gammaj();

    const Kokkos::View<const double*> kj = unknowns.kj();

    Kokkos::View<Rd*> uL = unknowns.uL();
    Kokkos::View<Rd*> uR = unknowns.uR();
    Kokkos::View<double*> kL = unknowns.kL();
    Kokkos::View<double*> kR = unknowns.kR();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();
    
    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();
    const Kokkos::View<const Rd**> Cjr = m_mesh_data.Cjr();

    // Calcule les flux
    computeExplicitFluxes(uj, Cjr, kj, uL, uR, kL, kR, t);

    const Kokkos::View<const Rdd*> Fl  = m_Fl ;
    const Kokkos::View<const Rd *> Gl  = m_Gl ;
    
    const Kokkos::View<const unsigned short*>& cell_nb_faces
      = m_connectivity.cellNbFaces();

    const Kokkos::View<const unsigned int*[2]>& cell_faces
      = m_connectivity.cellFaces();

    // Mise a jour de la vitesse et de l'energie totale specifique
    const Kokkos::View<const double*> inv_mj = unknowns.invMj();
    Kokkos::parallel_for(m_mesh.numberOfCells(), KOKKOS_LAMBDA(const int& j) {
	Rd momentum_fluxes = zero;
	double energy_fluxes = 0.;
	int l = 0;
	for (int R=0; R<cell_nb_faces(j); ++R) {
	  l = cell_faces(j,R);
	  momentum_fluxes +=  Fl(l)*Cjr(j,R);
	  energy_fluxes   += (Gl(l), Cjr(j,R));
	}
    
	uj[j] += (dt*inv_mj[j]) * momentum_fluxes;
	Ej[j] +=  (dt*inv_mj[j]) * energy_fluxes;
	//uj[j] += std::exp(-t)*(dt*inv_mj[j])*Vj(j)*Sj(j) + (dt*inv_mj[j]) * momentum_fluxes; // test avec k non constant

	// ajout second membre pour kidder (k = 0.5)
	//Ej[j] -= (dt*inv_mj[j])*Vj(j)*((0.5*t*t)/(((50./9.)-t*t)*((50./9.)-t*t)));

	// ajout second membre pour kidder (k = x)
	uj[j][0] += (dt*inv_mj[j])*Vj(j)*(t/((50./9.)-t*t)); 
	Ej[j] -= (dt*inv_mj[j])*Vj(j)*((2.*xj[j][0]*t*t)/(((50./9.)-t*t)*((50./9.)-t*t)));

      });

    // Calcul de e par la formule e = E-0.5 u^2 
    Kokkos::parallel_for(m_mesh.numberOfCells(), KOKKOS_LAMBDA(const int& j) {
	ej[j] = Ej[j] - 0.5 * (uj[j],uj[j]);
      });

    // met a jour les quantites (geometriques) associees au maillage
    //m_mesh_data.updateAllData();

    /*
    // Calcul de rho avec la formule Mj = Vj rhoj
    const Kokkos::View<const double*> mj = unknowns.mj();
    Kokkos::parallel_for(m_mesh.numberOfCells(), KOKKOS_LAMBDA(const int& j){
	rhoj[j] = mj[j]/Vj[j];
	
      });
    */
  }

  // Calcul erreur entre solution analytique et solution numerique en norme L2
  // (quand la solution exacte est connue)

  double error_L2_u(UnknownsType& unknowns, const double& t) {

    Kokkos::View<Rd*> uj = unknowns.uj();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();

    //double pi = 4.*std::atan(1.);
    double err_u = 0.;
    double exact_u = 0.;
    for (size_t j=0; j<m_mesh.numberOfCells(); ++j) {
      //exact_u = std::sin(pi*xj[j][0])*std::exp(-2.*pi*pi*0.2); // solution exacte cas test k constant
      // exact_u = std::sin(pi*xj[j][0])*std::exp(-0.2); // solution exacte cas test k non constant
      exact_u = -(xj[j][0]*t)/((50./9.)-t*t);
      err_u += (exact_u - uj[j][0])*(exact_u - uj[j][0])*Vj(j);
    }
    err_u = std::sqrt(err_u);
    return err_u;
  }

  double error_L2_rho(UnknownsType& unknowns, const double& t) {

    Kokkos::View<double*> rhoj = unknowns.rhoj();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();

    double h = std::sqrt(1. - (t*t)/(50./9.));
    double err_rho = 0.;
    double exact_rho = 0.;
    for (size_t j=0; j<m_mesh.numberOfCells(); ++j) {
      exact_rho = std::sqrt((3.*((xj[j][0]*xj[j][0])/(h*h)) + 100.)/100.)/h;
      err_rho += (exact_rho - rhoj[j])*(exact_rho - rhoj[j])*Vj(j);
    }
    err_rho = std::sqrt(err_rho);
    return err_rho;
  }

  /*
  double error_L2_E(UnknownsType& unknowns) {

    Kokkos::View<double*> Ej = unknowns.Ej();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();

    double pi = 4.*std::atan(1.);
    double err_E = 0.;
    double exact_E = 0.;
    for (size_t j=0; j<m_mesh.numberOfCells(); ++j) {
      //exact_E = (-(std::cos(pi*xj[j][0])*std::cos(pi*xj[j][0]))+(std::sin(pi*xj[j][0])*std::sin(pi*xj[j][0])))*0.5*(std::exp(-4.*pi*pi*0.2)-1.) + 2.;
      exact_E =  ((xj[j][0]*pi*pi*0.5)*(std::sin(pi*xj[j][0])*std::sin(pi*xj[j][0]) - std::cos(xj[j][0]*pi)*std::cos(pi*xj[j][0])) - pi*0.5*std::sin(pi*xj[j][0])*std::cos(pi*xj[j][0]))*(std::exp(-2.*0.2)-1.) + 2.;
      err_E += (exact_E - Ej[j])*(exact_E - Ej[j])*Vj(j);
    }
    err_E = std::sqrt(err_E);
    return err_E;
  }
  */

  // Calcul erreur entre solution analytique et solution numerique en norme L infini (max)
  // (quand la solution exacte est connue)

  double error_Linf(UnknownsType& unknowns, const double& t) {

    Kokkos::View<double*> rhoj = unknowns.rhoj();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    //double pi = 4.*std::atan(1.);
    double h = std::sqrt(1. - (t*t)/(50./9.));
    double exacte = std::sqrt((4.*((xj[0][0]*xj[0][0])/(h*h)) + 100.-(xj[0][0]*xj[0][0])/(h*h))/100.)/h;
    double erreur = std::abs(exacte - rhoj[0]);

    for (size_t j=1; j<m_mesh.numberOfCells(); ++j) {
      exacte = std::sqrt((3.*((xj[j][0]*xj[j][0])/(h*h)) + 100.)/100.)/h;
      if (std::abs(exacte - rhoj[j]) > erreur) {
	erreur = std::abs(exacte - rhoj[j]);
      }
    }

    return erreur;
  }

  // Verifie la conservativite de E

  double conservatif(UnknownsType& unknowns) {
   
    Kokkos::View<double*> Ej = unknowns.Ej();
    Kokkos::View<double*> rhoj = unknowns.rhoj();

    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    double sum = 0.;

    for (size_t j=0; j<m_mesh.numberOfCells(); ++j) {
      sum += Ej[j]*rhoj[j]*Vj[j];
    }

    return sum;
   
  }
    
  // Verifie la conservativite de quantite de mvt

  double conservatif_mvt(UnknownsType& unknowns) {
   
    Kokkos::View<double*> rhoj = unknowns.rhoj();
    Kokkos::View<Rd*> uj = unknowns.uj();

    const Kokkos::View<const double*> Vj = m_mesh_data.Vj();

    const Kokkos::View<const Rd*> xj = m_mesh_data.xj();

    double sum = 0.;

    for (size_t j=0; j<m_mesh.numberOfCells(); ++j) {
      sum += Vj[j]*rhoj[j]*uj[j][0];
    }

    return sum;
   
  }
  
};

#endif // FINITE_VOLUMES_DIFFUSION_HPP