Skip to content
Snippets Groups Projects
Select Git revision
  • 802ef9a927e3aaacb0c8568d9e2e0e5ac5cae59a
  • develop default protected
  • feature/gmsh-reader
  • origin/stage/bouguettaia
  • feature/kinetic-schemes
  • feature/reconstruction
  • feature/local-dt-fsi
  • feature/composite-scheme-sources
  • feature/composite-scheme-other-fluxes
  • feature/serraille
  • feature/variational-hydro
  • feature/composite-scheme
  • hyperplastic
  • feature/polynomials
  • feature/gks
  • feature/implicit-solver-o2
  • feature/coupling_module
  • feature/implicit-solver
  • feature/merge-local-dt-fsi
  • master protected
  • feature/escobar-smoother
  • v0.5.0 protected
  • v0.4.1 protected
  • v0.4.0 protected
  • v0.3.0 protected
  • v0.2.0 protected
  • v0.1.0 protected
  • Kidder
  • v0.0.4 protected
  • v0.0.3 protected
  • v0.0.2 protected
  • v0 protected
  • v0.0.1 protected
33 results

UnaryOperatorRegisterForR2.hpp

Blame
  • HybridHLLcRusanovEulerianCompositeSolver_v2.cpp 80.69 KiB
    #include <scheme/HybridHLLcRusanovEulerianCompositeSolver_v2.hpp>
    
    #include <language/utils/InterpolateItemArray.hpp>
    #include <mesh/Mesh.hpp>
    #include <mesh/MeshData.hpp>
    #include <mesh/MeshDataManager.hpp>
    #include <mesh/MeshEdgeBoundary.hpp>
    #include <mesh/MeshFaceBoundary.hpp>
    #include <mesh/MeshFlatEdgeBoundary.hpp>
    #include <mesh/MeshFlatFaceBoundary.hpp>
    #include <mesh/MeshFlatNodeBoundary.hpp>
    #include <mesh/MeshNodeBoundary.hpp>
    #include <mesh/MeshTraits.hpp>
    #include <mesh/MeshVariant.hpp>
    #include <mesh/SubItemValuePerItemUtils.hpp>
    #include <scheme/DiscreteFunctionUtils.hpp>
    #include <scheme/InflowListBoundaryConditionDescriptor.hpp>
    #include <variant>
    
    template <MeshConcept MeshTypeT>
    class HybridHLLcRusanovEulerianCompositeSolver_v2
    {
     private:
      using MeshType = MeshTypeT;
    
      static constexpr size_t Dimension = MeshType::Dimension;
    
      using Rdxd = TinyMatrix<Dimension>;
      using Rd   = TinyVector<Dimension>;
    
      using Rpxp = TinyMatrix<Dimension + 2>;
      using Rp   = TinyVector<Dimension + 2>;
    
      class SymmetryBoundaryCondition;
      class InflowListBoundaryCondition;
      class OutflowBoundaryCondition;
      class WallBoundaryCondition;
      class NeumannflatBoundaryCondition;
    
      using BoundaryCondition = std::variant<SymmetryBoundaryCondition,
                                             InflowListBoundaryCondition,
                                             OutflowBoundaryCondition,
                                             NeumannflatBoundaryCondition,
                                             WallBoundaryCondition>;
    
      using BoundaryConditionList = std::vector<BoundaryCondition>;
    
      BoundaryConditionList
      _getBCList(const MeshType& mesh,
                 const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>& bc_descriptor_list) const
      {
        BoundaryConditionList bc_list;
    
        for (const auto& bc_descriptor : bc_descriptor_list) {
          bool is_valid_boundary_condition = true;
    
          switch (bc_descriptor->type()) {
          case IBoundaryConditionDescriptor::Type::wall: {
            if constexpr (Dimension == 2) {
              bc_list.emplace_back(WallBoundaryCondition(getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                                         getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            } else {
              static_assert(Dimension == 3);
              bc_list.emplace_back(WallBoundaryCondition(getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                                         getMeshEdgeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                                         getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            }
            break;
          }
          case IBoundaryConditionDescriptor::Type::symmetry: {
            if constexpr (Dimension == 2) {
              bc_list.emplace_back(
                SymmetryBoundaryCondition(getMeshFlatNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                          getMeshFlatFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            } else {
              static_assert(Dimension == 3);
              bc_list.emplace_back(
                SymmetryBoundaryCondition(getMeshFlatNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                          getMeshFlatEdgeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                          getMeshFlatFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            }
            break;
          }
          case IBoundaryConditionDescriptor::Type::inflow_list: {
            const InflowListBoundaryConditionDescriptor& inflow_list_bc_descriptor =
              dynamic_cast<const InflowListBoundaryConditionDescriptor&>(*bc_descriptor);
            if (inflow_list_bc_descriptor.functionSymbolIdList().size() != 2 + Dimension) {
              std::ostringstream error_msg;
              error_msg << "invalid number of functions for inflow boundary "
                        << inflow_list_bc_descriptor.boundaryDescriptor() << ", found "
                        << inflow_list_bc_descriptor.functionSymbolIdList().size() << ", expecting " << 2 + Dimension;
              throw NormalError(error_msg.str());
            }
    
            if constexpr (Dimension == 2) {
              auto node_boundary = getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor());
              Table<const double> node_values =
                InterpolateItemArray<double(Rd)>::template interpolate<ItemType::node>(inflow_list_bc_descriptor
                                                                                         .functionSymbolIdList(),
                                                                                       mesh.xr(), node_boundary.nodeList());
    
              auto xl = MeshDataManager::instance().getMeshData(mesh).xl();
    
              auto face_boundary = getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor());
              Table<const double> face_values =
                InterpolateItemArray<double(Rd)>::template interpolate<ItemType::face>(inflow_list_bc_descriptor
                                                                                         .functionSymbolIdList(),
                                                                                       xl, face_boundary.faceList());
    
              bc_list.emplace_back(InflowListBoundaryCondition(node_boundary, face_boundary, node_values, face_values));
            } else {
              static_assert(Dimension == 3);
              auto node_boundary = getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor());
              Table<const double> node_values =
                InterpolateItemArray<double(Rd)>::template interpolate<ItemType::node>(inflow_list_bc_descriptor
                                                                                         .functionSymbolIdList(),
                                                                                       mesh.xr(), node_boundary.nodeList());
    
              auto xe = MeshDataManager::instance().getMeshData(mesh).xe();
    
              auto edge_boundary = getMeshEdgeBoundary(mesh, bc_descriptor->boundaryDescriptor());
              Table<const double> edge_values =
                InterpolateItemArray<double(Rd)>::template interpolate<ItemType::edge>(inflow_list_bc_descriptor
                                                                                         .functionSymbolIdList(),
                                                                                       xe, edge_boundary.edgeList());
    
              auto xl = MeshDataManager::instance().getMeshData(mesh).xl();
    
              auto face_boundary = getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor());
              Table<const double> face_values =
                InterpolateItemArray<double(Rd)>::template interpolate<ItemType::face>(inflow_list_bc_descriptor
                                                                                         .functionSymbolIdList(),
                                                                                       xl, face_boundary.faceList());
    
              bc_list.emplace_back(InflowListBoundaryCondition(node_boundary, edge_boundary, face_boundary, node_values,
                                                               edge_values, face_values));
            }
            break;
          }
          case IBoundaryConditionDescriptor::Type::outflow: {
            if constexpr (Dimension == 2) {
              bc_list.emplace_back(
                OutflowBoundaryCondition(getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                         getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            } else {
              static_assert(Dimension == 3);
              bc_list.emplace_back(
                OutflowBoundaryCondition(getMeshNodeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                         getMeshEdgeBoundary(mesh, bc_descriptor->boundaryDescriptor()),
                                         getMeshFaceBoundary(mesh, bc_descriptor->boundaryDescriptor())));
            }
            break;
            // std::cout << "outflow not implemented yet\n";
            // break;
          }
          default: {
            is_valid_boundary_condition = false;
          }
          }
          if (not is_valid_boundary_condition) {
            std::ostringstream error_msg;
            error_msg << *bc_descriptor << " is an invalid boundary condition for Rusanov v2 Eulerian Composite solver";
            throw NormalError(error_msg.str());
          }
        }
    
        return bc_list;
      }
    
     public:
      void
      _applyWallBoundaryCondition(const BoundaryConditionList& bc_list,
                                  const MeshType& mesh,
                                  NodeValuePerCell<Rp>& stateNode,
                                  EdgeValuePerCell<Rp>& stateEdge,
                                  FaceValuePerCell<Rp>& stateFace) const
      {
        for (const auto& boundary_condition : bc_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<WallBoundaryCondition, T>) {
                MeshData<MeshType>& mesh_data = MeshDataManager::instance().getMeshData(mesh);
                std::cout << " Traitement WALL local (non flat) \n";
                // const Rd& normal = bc.outgoingNormal();
    
                const auto& node_to_cell_matrix = mesh.connectivity().nodeToCellMatrix();
                const auto& node_to_face_matrix = mesh.connectivity().nodeToFaceMatrix();
                const auto& face_to_cell_matrix = mesh.connectivity().faceToCellMatrix();
    
                const auto& node_local_numbers_in_their_cells = mesh.connectivity().nodeLocalNumbersInTheirCells();
                const auto& node_local_numbers_in_their_faces = mesh.connectivity().nodeLocalNumbersInTheirFaces();
                const auto& face_local_numbers_in_their_cells = mesh.connectivity().faceLocalNumbersInTheirCells();
                // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                const auto& face_list = bc.faceList();
                const auto& node_list = bc.nodeList();
    
                // const auto Cjr = mesh_data.Cjr();
                const auto Cjf = mesh_data.Cjf();
    
                for (size_t i_node = 0; i_node < node_list.size(); ++i_node) {
                  const NodeId node_id = node_list[i_node];
    
                  const auto& node_face_list = node_to_face_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  // const auto& node_local_number_in_its_faces = node_local_numbers_in_their_faces.itemArray(node_id);
    
                  // on va chercher les normale d'une face issue du noeud de CL et contenue dans le faceList
                  Rd normal(zero);
                  int nbnormal = 0;
                  for (size_t i_face = 0; i_face < node_face_list.size(); ++i_face) {
                    FaceId node_face_id = node_face_list[i_face];
    
                    for (size_t i_facebc = 0; i_facebc < face_list.size(); ++i_facebc) {
                      const FaceId facebc_id = face_list[i_facebc];
                      if (node_face_id == facebc_id) {
                        const auto& face_cell_list = face_to_cell_matrix[facebc_id];
                        Assert(face_cell_list.size() == 1);
    
                        CellId face_cell_id              = face_cell_list[0];
                        size_t face_local_number_in_cell = face_local_numbers_in_their_cells(facebc_id, 0);
    
                        // Normal locale approchée
                        Rd normalloc = Cjf(face_cell_id, face_local_number_in_cell);
                        normalloc *= 1. / l2Norm(normalloc);
                        normal += normalloc;
                        ++nbnormal;
                        break;
                      }
                    }
                  }
                  if (nbnormal == 0)
                    continue;
                  normal *= 1. / nbnormal;
    
                  normal *= 1. / l2Norm(normal);
                  const auto& node_cell_list = node_to_cell_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node_id);
    
                  for (size_t i_cell = 0; i_cell < node_cell_list.size(); ++i_cell) {
                    CellId node_cell_id              = node_cell_list[i_cell];
                    size_t node_local_number_in_cell = node_local_number_in_its_cells[i_cell];
    
                    Rd vectorSym(zero);
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      vectorSym[dim] = stateNode[node_cell_id][node_local_number_in_cell][1 + dim];
    
                    vectorSym -= dot(vectorSym, normal) * normal;
    
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim + 1] = vectorSym[dim];
                    // stateNode[node_cell_id][node_local_number_in_cell][dim + 1] = 0;
                  }
                }
    
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
    
                  const auto& face_cell_list = face_to_cell_matrix[face_id];
                  Assert(face_cell_list.size() == 1);
    
                  CellId face_cell_id              = face_cell_list[0];
                  size_t face_local_number_in_cell = face_local_numbers_in_their_cells(face_id, 0);
    
                  // Normal locale approchée
                  Rd normal(Cjf(face_cell_id, face_local_number_in_cell));
                  normal *= 1. / l2Norm(normal);
    
                  Rd vectorSym(zero);
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    vectorSym[dim] = stateFace[face_cell_id][face_local_number_in_cell][1 + dim];
    
                  vectorSym -= dot(vectorSym, normal) * normal;
    
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    stateFace[face_cell_id][face_local_number_in_cell][dim + 1] = vectorSym[dim];
                  // stateFace[face_cell_id][face_local_number_in_cell][dim + 1] = 0;
                }
    
                if constexpr (Dimension == 3) {
                  const auto& edge_to_cell_matrix = mesh.connectivity().edgeToCellMatrix();
    
                  const auto& edge_local_numbers_in_their_cells = mesh.connectivity().edgeLocalNumbersInTheirCells();
    
                  const auto& edge_to_face_matrix = mesh.connectivity().edgeToFaceMatrix();
    
                  const auto& edge_local_numbers_in_their_faces = mesh.connectivity().edgeLocalNumbersInTheirFaces();
    
                  const auto& edge_list = bc.edgeList();
    
                  for (size_t i_edge = 0; i_edge < edge_list.size(); ++i_edge) {
                    const EdgeId edge_id       = edge_list[i_edge];
                    const auto& edge_face_list = edge_to_face_matrix[edge_id];
    
                    // on va chercher les normale d'une face issue du edge de CL et contenue dans le faceList
                    Rd normal(zero);
                    int nbnormal = 0;
                    for (size_t i_face = 0; i_face < edge_face_list.size(); ++i_face) {
                      FaceId edge_face_id = edge_face_list[i_face];
    
                      for (size_t i_facebc = 0; i_facebc < face_list.size(); ++i_facebc) {
                        const FaceId facebc_id = face_list[i_facebc];
                        if (edge_face_id == facebc_id) {
                          const auto& face_cell_list = face_to_cell_matrix[facebc_id];
                          Assert(face_cell_list.size() == 1);
    
                          CellId face_cell_id              = face_cell_list[0];
                          size_t face_local_number_in_cell = face_local_numbers_in_their_cells(facebc_id, 0);
    
                          // Normal locale approchée
                          Rd normalloc = Cjf(face_cell_id, face_local_number_in_cell);
                          normalloc *= 1. / l2Norm(normalloc);
                          normal += normalloc;
                          ++nbnormal;
                          break;
                        }
                      }
                    }
    
                    if (nbnormal == 0)
                      continue;
                    normal *= 1. / nbnormal;
    
                    normal *= 1. / l2Norm(normal);
    
                    const auto& edge_cell_list = edge_to_cell_matrix[edge_id];
    
                    const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge_id);
    
                    for (size_t i_cell = 0; i_cell < edge_cell_list.size(); ++i_cell) {
                      CellId edge_cell_id              = edge_cell_list[i_cell];
                      size_t edge_local_number_in_cell = edge_local_number_in_its_cells[i_cell];
    
                      Rd vectorSym(zero);
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        vectorSym[dim] = stateEdge[edge_cell_id][edge_local_number_in_cell][1 + dim];
    
                      vectorSym -= dot(vectorSym, normal) * normal;
    
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        stateEdge[edge_cell_id][edge_local_number_in_cell][dim + 1] = vectorSym[dim];
                      // stateEdge[edge_cell_id][edge_local_number_in_cell][dim + 1] = 0;
                    }
                  }
                }
              }
            },
            boundary_condition);
        }
      }
    
      void
      _applyOutflowBoundaryCondition(const BoundaryConditionList& bc_list,
                                     const MeshType& mesh,
                                     NodeValuePerCell<Rp>& stateNode,
                                     EdgeValuePerCell<Rp>& stateEdge,
                                     FaceValuePerCell<Rp>& stateFace) const
      {
        for (const auto& boundary_condition : bc_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<OutflowBoundaryCondition, T>) {
                std::cout << " Traitement Outflow  \n";
                // const Rd& normal = bc.outgoingNormal();
                /*
                const auto& node_to_cell_matrix = mesh.connectivity().nodeToCellMatrix();
                const auto& face_to_cell_matrix = mesh.connectivity().faceToCellMatrix();
    
                const auto& node_local_numbers_in_their_cells = mesh.connectivity().nodeLocalNumbersInTheirCells();
                const auto& face_local_numbers_in_their_cells = mesh.connectivity().faceLocalNumbersInTheirCells();
                // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                const auto& face_list = bc.faceList();
                const auto& node_list = bc.nodeList();
    
                const auto xj = mesh.xj();
                const auto xr = mesh.xr();
                const auto xf = mesh.xl();
                const auto xe = mesh.xe();
    
                for (size_t i_node = 0; i_node < node_list.size(); ++i_node) {
                  const NodeId node_id = node_list[i_node];
    
                  const auto& node_cell_list = node_to_cell_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node_id);
    
                  for (size_t i_cell = 0; i_cell < node_cell_list.size(); ++i_cell) {
                    CellId node_cell_id              = node_cell_list[i_cell];
                    size_t node_local_number_in_cell = node_local_number_in_its_cells[i_cell];
    
                    for (size_t dim = 0; dim < Dimension + 2; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim] += vectorSym[dim];
    
                    Rd vectorSym(zero);
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      vectorSym[dim] = stateNode[node_cell_id][node_local_number_in_cell][1 + dim];
    
                    Rdxd MatriceProj(identity);
                    MatriceProj -= tensorProduct(normal, normal);
                    vectorSym = MatriceProj * vectorSym;
    
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim + 1] = vectorSym[dim];
                    //  stateNode[node_cell_id][node_local_number_in_cell][dim] = 0;   // node_array_list[i_node][dim];
                  }
                }
    
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
    
                  const auto& face_cell_list = face_to_cell_matrix[face_id];
                  Assert(face_cell_list.size() == 1);
    
                  CellId face_cell_id              = face_cell_list[0];
                  size_t face_local_number_in_cell = face_local_numbers_in_their_cells(face_id, 0);
    
                  Rd vectorSym(zero);
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    vectorSym[dim] = stateEdge[face_cell_id][face_local_number_in_cell][1 + dim];
    
                  Rdxd MatriceProj(identity);
                  MatriceProj -= tensorProduct(normal, normal);
                  vectorSym = MatriceProj * vectorSym;
    
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    stateFace[face_cell_id][face_local_number_in_cell][dim + 1] = vectorSym[dim];
                }
    
                if constexpr (Dimension == 3) {
                  const auto& edge_to_cell_matrix = mesh.connectivity().edgeToCellMatrix();
    
                  const auto& edge_local_numbers_in_their_cells = mesh.connectivity().edgeLocalNumbersInTheirCells();
    
                  const auto& edge_list = bc.edgeList();
    
                  for (size_t i_edge = 0; i_edge < edge_list.size(); ++i_edge) {
                    const EdgeId edge_id = edge_list[i_edge];
    
                    const auto& edge_cell_list = edge_to_cell_matrix[edge_id];
                    // Assert(face_cell_list.size() == 1);
                    const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge_id);
    
                    for (size_t i_cell = 0; i_cell < edge_cell_list.size(); ++i_cell) {
                      CellId edge_cell_id              = edge_cell_list[i_cell];
                      size_t edge_local_number_in_cell = edge_local_number_in_its_cells[i_cell];
    
                      Rd vectorSym(zero);
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        vectorSym[dim] = stateEdge[edge_cell_id][edge_local_number_in_cell][1 + dim];
    
                      Rdxd MatriceProj(identity);
                      MatriceProj -= tensorProduct(normal, normal);
                      vectorSym = MatriceProj * vectorSym;
    
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        stateEdge[edge_cell_id][edge_local_number_in_cell][dim + 1] = vectorSym[dim];
                    }
                  }
    
                  //          throw NormalError("Not implemented");
                }
                */
              }
            },
            boundary_condition);
        }
      }
    
      void
      _applySymmetricBoundaryCondition(const BoundaryConditionList& bc_list,
                                       const MeshType& mesh,
                                       NodeValuePerCell<Rp>& stateNode,
                                       EdgeValuePerCell<Rp>& stateEdge,
                                       FaceValuePerCell<Rp>& stateFace) const
      {
        for (const auto& boundary_condition : bc_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<SymmetryBoundaryCondition, T>) {
                // MeshData<MeshType>& mesh_data = MeshDataManager::instance().getMeshData(mesh);
                std::cout << " Traitement SYMMETRY  \n";
                const Rd& normal = bc.outgoingNormal();
    
                const auto& node_to_cell_matrix = mesh.connectivity().nodeToCellMatrix();
                const auto& face_to_cell_matrix = mesh.connectivity().faceToCellMatrix();
    
                const auto& node_local_numbers_in_their_cells = mesh.connectivity().nodeLocalNumbersInTheirCells();
                const auto& face_local_numbers_in_their_cells = mesh.connectivity().faceLocalNumbersInTheirCells();
                // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                const auto& face_list = bc.faceList();
                const auto& node_list = bc.nodeList();
    
                for (size_t i_node = 0; i_node < node_list.size(); ++i_node) {
                  const NodeId node_id = node_list[i_node];
    
                  const auto& node_cell_list = node_to_cell_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node_id);
    
                  for (size_t i_cell = 0; i_cell < node_cell_list.size(); ++i_cell) {
                    CellId node_cell_id              = node_cell_list[i_cell];
                    size_t node_local_number_in_cell = node_local_number_in_its_cells[i_cell];
    
                    Rd vectorSym(zero);
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      vectorSym[dim] = stateNode[node_cell_id][node_local_number_in_cell][1 + dim];
    
                    Rdxd MatriceProj(identity);
                    MatriceProj -= tensorProduct(normal, normal);
                    vectorSym = MatriceProj * vectorSym;
    
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim + 1] = vectorSym[dim];
                    //  stateNode[node_cell_id][node_local_number_in_cell][dim] = 0;   // node_array_list[i_node][dim];
                  }
                }
    
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
    
                  const auto& face_cell_list = face_to_cell_matrix[face_id];
                  Assert(face_cell_list.size() == 1);
    
                  CellId face_cell_id              = face_cell_list[0];
                  size_t face_local_number_in_cell = face_local_numbers_in_their_cells(face_id, 0);
    
                  Rd vectorSym(zero);
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    vectorSym[dim] = stateFace[face_cell_id][face_local_number_in_cell][1 + dim];
    
                  Rdxd MatriceProj(identity);
                  MatriceProj -= tensorProduct(normal, normal);
                  vectorSym = MatriceProj * vectorSym;
    
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    stateFace[face_cell_id][face_local_number_in_cell][dim + 1] = vectorSym[dim];
                }
    
                if constexpr (Dimension == 3) {
                  const auto& edge_to_cell_matrix = mesh.connectivity().edgeToCellMatrix();
    
                  const auto& edge_local_numbers_in_their_cells = mesh.connectivity().edgeLocalNumbersInTheirCells();
    
                  const auto& edge_list = bc.edgeList();
    
                  for (size_t i_edge = 0; i_edge < edge_list.size(); ++i_edge) {
                    const EdgeId edge_id = edge_list[i_edge];
    
                    const auto& edge_cell_list = edge_to_cell_matrix[edge_id];
                    // Assert(face_cell_list.size() == 1);
                    const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge_id);
    
                    for (size_t i_cell = 0; i_cell < edge_cell_list.size(); ++i_cell) {
                      CellId edge_cell_id              = edge_cell_list[i_cell];
                      size_t edge_local_number_in_cell = edge_local_number_in_its_cells[i_cell];
    
                      Rd vectorSym(zero);
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        vectorSym[dim] = stateEdge[edge_cell_id][edge_local_number_in_cell][1 + dim];
    
                      Rdxd MatriceProj(identity);
                      MatriceProj -= tensorProduct(normal, normal);
                      vectorSym = MatriceProj * vectorSym;
    
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        stateEdge[edge_cell_id][edge_local_number_in_cell][dim + 1] = vectorSym[dim];
                    }
                  }
                }
              }
            },
            boundary_condition);
        }
      }
    
      void
      _applyNeumannflatBoundaryCondition(const BoundaryConditionList& bc_list,
                                         const MeshType& mesh,
                                         NodeValuePerCell<Rp>& stateNode,
                                         EdgeValuePerCell<Rp>& stateEdge,
                                         FaceValuePerCell<Rp>& stateFace) const
      {
        for (const auto& boundary_condition : bc_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<NeumannflatBoundaryCondition, T>) {
                // MeshData<MeshType>& mesh_data = MeshDataManager::instance().getMeshData(mesh);
                std::cout << " Traitement WALL  \n";
                const Rd& normal = bc.outgoingNormal();
    
                const auto& node_to_cell_matrix = mesh.connectivity().nodeToCellMatrix();
                const auto& face_to_cell_matrix = mesh.connectivity().faceToCellMatrix();
    
                const auto& node_local_numbers_in_their_cells = mesh.connectivity().nodeLocalNumbersInTheirCells();
                const auto& face_local_numbers_in_their_cells = mesh.connectivity().faceLocalNumbersInTheirCells();
                // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                const auto& face_list = bc.faceList();
                const auto& node_list = bc.nodeList();
    
                for (size_t i_node = 0; i_node < node_list.size(); ++i_node) {
                  const NodeId node_id = node_list[i_node];
    
                  const auto& node_cell_list = node_to_cell_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node_id);
    
                  for (size_t i_cell = 0; i_cell < node_cell_list.size(); ++i_cell) {
                    CellId node_cell_id              = node_cell_list[i_cell];
                    size_t node_local_number_in_cell = node_local_number_in_its_cells[i_cell];
    
                    Rd vectorSym(zero);
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      vectorSym[dim] = stateNode[node_cell_id][node_local_number_in_cell][1 + dim];
    
                    vectorSym -= dot(vectorSym, normal) * normal;
    
                    for (size_t dim = 0; dim < Dimension; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim + 1] = vectorSym[dim];
                    //  stateNode[node_cell_id][node_local_number_in_cell][dim] = 0;   // node_array_list[i_node][dim];
                  }
                }
    
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
    
                  const auto& face_cell_list = face_to_cell_matrix[face_id];
                  Assert(face_cell_list.size() == 1);
    
                  CellId face_cell_id              = face_cell_list[0];
                  size_t face_local_number_in_cell = face_local_numbers_in_their_cells(face_id, 0);
    
                  Rd vectorSym(zero);
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    vectorSym[dim] = stateFace[face_cell_id][face_local_number_in_cell][1 + dim];
    
                  vectorSym -= dot(vectorSym, normal) * normal;
    
                  for (size_t dim = 0; dim < Dimension; ++dim)
                    stateFace[face_cell_id][face_local_number_in_cell][dim + 1] = vectorSym[dim];
                }
    
                if constexpr (Dimension == 3) {
                  const auto& edge_to_cell_matrix = mesh.connectivity().edgeToCellMatrix();
    
                  const auto& edge_local_numbers_in_their_cells = mesh.connectivity().edgeLocalNumbersInTheirCells();
    
                  const auto& edge_list = bc.edgeList();
    
                  for (size_t i_edge = 0; i_edge < edge_list.size(); ++i_edge) {
                    const EdgeId edge_id = edge_list[i_edge];
    
                    const auto& edge_cell_list = edge_to_cell_matrix[edge_id];
                    // Assert(face_cell_list.size() == 1);
                    const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge_id);
    
                    for (size_t i_cell = 0; i_cell < edge_cell_list.size(); ++i_cell) {
                      CellId edge_cell_id              = edge_cell_list[i_cell];
                      size_t edge_local_number_in_cell = edge_local_number_in_its_cells[i_cell];
    
                      Rd vectorSym(zero);
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        vectorSym[dim] = stateEdge[edge_cell_id][edge_local_number_in_cell][1 + dim];
    
                      vectorSym -= dot(vectorSym, normal) * normal;
    
                      for (size_t dim = 0; dim < Dimension; ++dim)
                        stateEdge[edge_cell_id][edge_local_number_in_cell][dim + 1] = vectorSym[dim];
                    }
                  }
                }
              }
            },
            boundary_condition);
        }
      }
    
      void
      _applyInflowBoundaryCondition(const BoundaryConditionList& bc_list,
                                    const MeshType& mesh,
                                    NodeValuePerCell<Rp>& stateNode,
                                    EdgeValuePerCell<Rp>& stateEdge,
                                    FaceValuePerCell<Rp>& stateFace) const
      {
        for (const auto& boundary_condition : bc_list) {
          std::visit(
            [&](auto&& bc) {
              using T = std::decay_t<decltype(bc)>;
              if constexpr (std::is_same_v<InflowListBoundaryCondition, T>) {
                // MeshData<MeshType>& mesh_data = MeshDataManager::instance().getMeshData(mesh);
                std::cout << " Traitement INFLOW  \n";
    
                const auto& node_to_cell_matrix = mesh.connectivity().nodeToCellMatrix();
                const auto& face_to_cell_matrix = mesh.connectivity().faceToCellMatrix();
    
                const auto& node_local_numbers_in_their_cells = mesh.connectivity().nodeLocalNumbersInTheirCells();
                const auto& face_local_numbers_in_their_cells = mesh.connectivity().faceLocalNumbersInTheirCells();
                // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                const auto& face_list = bc.faceList();
                const auto& node_list = bc.nodeList();
    
                const auto& face_array_list = bc.faceArrayList();
                const auto& node_array_list = bc.nodeArrayList();
    
                for (size_t i_node = 0; i_node < node_list.size(); ++i_node) {
                  const NodeId node_id = node_list[i_node];
    
                  const auto& node_cell_list = node_to_cell_matrix[node_id];
                  // Assert(face_cell_list.size() == 1);
                  const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node_id);
    
                  for (size_t i_cell = 0; i_cell < node_cell_list.size(); ++i_cell) {
                    CellId node_cell_id              = node_cell_list[i_cell];
                    size_t node_local_number_in_cell = node_local_number_in_its_cells[i_cell];
    
                    for (size_t dim = 0; dim < Dimension + 2; ++dim)
                      stateNode[node_cell_id][node_local_number_in_cell][dim] = node_array_list[i_node][dim];
                  }
                }
    
                for (size_t i_face = 0; i_face < face_list.size(); ++i_face) {
                  const FaceId face_id = face_list[i_face];
    
                  const auto& face_cell_list = face_to_cell_matrix[face_id];
                  Assert(face_cell_list.size() == 1);
    
                  CellId face_cell_id              = face_cell_list[0];
                  size_t face_local_number_in_cell = face_local_numbers_in_their_cells(face_id, 0);
    
                  for (size_t dim = 0; dim < Dimension + 2; ++dim)
                    stateFace[face_cell_id][face_local_number_in_cell][dim] = face_array_list[i_face][dim];
                }
    
                if constexpr (Dimension == 3) {
                  const auto& edge_to_cell_matrix = mesh.connectivity().edgeToCellMatrix();
    
                  const auto& edge_local_numbers_in_their_cells = mesh.connectivity().edgeLocalNumbersInTheirCells();
                  // const auto& face_cell_is_reversed             = mesh.connectivity().cellFaceIsReversed();
    
                  const auto& edge_list = bc.edgeList();
    
                  const auto& edge_array_list = bc.edgeArrayList();
    
                  for (size_t i_edge = 0; i_edge < edge_list.size(); ++i_edge) {
                    const EdgeId edge_id = edge_list[i_edge];
    
                    const auto& edge_cell_list                 = edge_to_cell_matrix[edge_id];
                    const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge_id);
    
                    // Assert(face_cell_list.size() == 1);
    
                    for (size_t i_cell = 0; i_cell < edge_cell_list.size(); ++i_cell) {
                      CellId edge_cell_id              = edge_cell_list[i_cell];
                      size_t edge_local_number_in_cell = edge_local_number_in_its_cells[i_cell];
    
                      for (size_t dim = 0; dim < Dimension + 2; ++dim)
                        stateEdge[edge_cell_id][edge_local_number_in_cell][dim] = edge_array_list[i_edge][dim];
                    }
                  }
                }
              }
            },
            boundary_condition);
        }
      }
    
     public:
      inline double
      pression(const double rho, const double epsilon, const double gam) const
      {
        return (gam - 1) * rho * epsilon;
      }
    
      std::tuple<std::shared_ptr<const DiscreteFunctionVariant>,
                 std::shared_ptr<const DiscreteFunctionVariant>,
                 std::shared_ptr<const DiscreteFunctionVariant>>
      solve(const std::shared_ptr<const MeshType>& p_mesh,
            const DiscreteFunctionP0<const double>& rho_n,
            const DiscreteFunctionP0<const Rd>& u_n,
            const DiscreteFunctionP0<const double>& E_n,
            const double& gamma,
            const DiscreteFunctionP0<const double>& c_n,
            const DiscreteFunctionP0<const double>& p_n,
            // const size_t degree,
            const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>& bc_descriptor_list,
            const double& dt,
            const bool checkLocalConservation) const
      {
        auto rho = copy(rho_n);
        auto u   = copy(u_n);
        auto E   = copy(E_n);
        // auto c   = copy(c_n);
        // auto p   = copy(p_n);
    
        auto bc_list = this->_getBCList(*p_mesh, bc_descriptor_list);
    
        auto rhoE = rho * E;
        auto rhoU = rho * u;
    
        // Construction du vecteur des variables conservatives
        //
        // Ci dessous juste ordre 1
        //
        CellValue<Rp> State{p_mesh->connectivity()};
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            State[j][0] = rho[j];
            for (size_t d = 0; d < Dimension; ++d)
              State[j][1 + d] = rhoU[j][d];
            State[j][1 + Dimension] = rhoE[j];
          });
    
        // CellValue<Rp> State{p_mesh->connectivity()};
        //
        // Remplir ici les reconstructions d'ordre élevé
    
        //
        const auto& cell_to_node_matrix = p_mesh->connectivity().cellToNodeMatrix();
        const auto& cell_to_edge_matrix = p_mesh->connectivity().cellToEdgeMatrix();
        const auto& cell_to_face_matrix = p_mesh->connectivity().cellToFaceMatrix();
    
        //    const auto xr = p_mesh->xr();
        // auto xl       = MeshDataManager::instance().getMeshData(*p_mesh).xl();
        // auto xe       = MeshDataManager::instance().getMeshData(*p_mesh).xe();
    
        NodeValuePerCell<Rp> StateAtNode{p_mesh->connectivity()};
        StateAtNode.fill(zero);
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) { StateAtNode[j].fill(State[j]); });
    
        EdgeValuePerCell<Rp> StateAtEdge{p_mesh->connectivity()};
        StateAtEdge.fill(zero);
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) { StateAtEdge[j].fill(State[j]); });
        FaceValuePerCell<Rp> StateAtFace{p_mesh->connectivity()};
        StateAtFace.fill(zero);
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) { StateAtFace[j].fill(State[j]); });
    
        // Conditions aux limites des etats conservatifs
    
        _applyInflowBoundaryCondition(bc_list, *p_mesh, StateAtNode, StateAtEdge, StateAtFace);
        //_applyOutflowBoundaryCondition(bc_list, *p_mesh, StateAtNode, StateAtEdge, StateAtFace);
        _applySymmetricBoundaryCondition(bc_list, *p_mesh, StateAtNode, StateAtEdge, StateAtFace);
        _applyNeumannflatBoundaryCondition(bc_list, *p_mesh, StateAtNode, StateAtEdge, StateAtFace);
        _applyWallBoundaryCondition(bc_list, *p_mesh, StateAtNode, StateAtEdge, StateAtFace);
    
        //
        // Construction du flux .. ok pour l'ordre 1
        //
        CellValue<Rdxd> rhoUtensU{p_mesh->connectivity()};
        CellValue<Rdxd> Pid(p_mesh->connectivity());
        Pid.fill(identity);
        CellValue<Rdxd> rhoUtensUPlusPid{p_mesh->connectivity()};
        rhoUtensUPlusPid.fill(zero);
    
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            rhoUtensU[j] = tensorProduct(rhoU[j], u[j]);
            Pid[j] *= p_n[j];
            rhoUtensUPlusPid[j] = rhoUtensU[j] + Pid[j];
          });
    
        auto Flux_rho    = rhoU;
        auto Flux_qtmvt  = rhoUtensUPlusPid;   // rhoUtensU + Pid;
        auto Flux_totnrj = (rhoE + p_n) * u;
    
        // Flux avec prise en compte des states at Node/Edge/Face
    
        NodeValuePerCell<Rd> Flux_rhoAtCellNode{p_mesh->connectivity()};
        EdgeValuePerCell<Rd> Flux_rhoAtCellEdge{p_mesh->connectivity()};
        FaceValuePerCell<Rd> Flux_rhoAtCellFace{p_mesh->connectivity()};
        /*
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            const auto& cell_to_node = cell_to_node_matrix[j];
    
            for (size_t l = 0; l < cell_to_node.size(); ++l) {
              for (size_t dim = 0; dim < Dimension; ++dim)
                Flux_rhoAtCellNode[j][l][dim] = StateAtNode[j][l][0] * StateAtNode[j][l][dim];
            }
    
            const auto& cell_to_face = cell_to_face_matrix[j];
    
            for (size_t l = 0; l < cell_to_face.size(); ++l) {
              for (size_t dim = 0; dim < Dimension; ++dim)
                Flux_rhoAtCellFace[j][l][dim] = StateAtFace[j][l][0] * StateAtFace[j][l][dim];
            }
    
            const auto& cell_to_edge = cell_to_edge_matrix[j];
    
            for (size_t l = 0; l < cell_to_edge.size(); ++l) {
              for (size_t dim = 0; dim < Dimension; ++dim)
                Flux_rhoAtCellEdge[j][l][dim] = StateAtEdge[j][l][0] * StateAtEdge[j][l][dim];
            }
          });
      */
        NodeValuePerCell<Rdxd> Flux_qtmvtAtCellNode{p_mesh->connectivity()};   // = rhoUtensUPlusPid;   // rhoUtensU + Pid;
        EdgeValuePerCell<Rdxd> Flux_qtmvtAtCellEdge{p_mesh->connectivity()};   // = rhoUtensUPlusPid;   // rhoUtensU + Pid;
        FaceValuePerCell<Rdxd> Flux_qtmvtAtCellFace{p_mesh->connectivity()};   // = rhoUtensUPlusPid;   // rhoUtensU + Pid;
                                                                               /*
                                                                               parallel_for(
                                                                                 p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
                                                                                   const auto& cell_to_node = cell_to_node_matrix[j];
                                                                           for (size_t l = 0; l < cell_to_node.size(); ++l) {
                                                                                       for (size_t dim = 0; dim < Dimension; ++dim)
                                                                                         Flux_qtmvtAtCellNode[j][l][dim] = StateAtNode[j][l][0] * StateAtNode[j][l][dim];
                                                                                     }
    
                                                                                     const auto& cell_to_face = cell_to_face_matrix[j];
    
                                                                                     for (size_t l = 0; l < cell_to_face.size(); ++l) {
                                                                                       for (size_t dim = 0; dim < Dimension; ++dim)
                                                                                         Flux_qtmvtAtCellFace[j][l][dim] = StateAtFace[j][l][0] * StateAtFace[j][l][dim];
                                                                                     }
    
                                                                                     const auto& cell_to_edge = cell_to_edge_matrix[j];
    
                                                                                     for (size_t l = 0; l < cell_to_edge.size(); ++l) {
                                                                                       for (size_t dim = 0; dim < Dimension; ++dim)
                                                                                         Flux_qtmvtAtCellEdge[j][l][dim] = StateAtEdge[j][l][0] * StateAtEdge[j][l][dim];
                                                                                     }
                                                                                   });
                                                                               */
        // parallel_for(
        //   p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
        //     Flux_qtmvtAtCellNode[j] = Flux_qtmvtAtCellEdge[j] = Flux_qtmvtAtCellFace[j] = Flux_qtmvt[j];
        //   });
    
        NodeValuePerCell<Rd> Flux_totnrjAtCellNode{p_mesh->connectivity()};
        EdgeValuePerCell<Rd> Flux_totnrjAtCellEdge{p_mesh->connectivity()};
        FaceValuePerCell<Rd> Flux_totnrjAtCellFace{p_mesh->connectivity()};
    
        Flux_rhoAtCellEdge.fill(zero);
        Flux_totnrjAtCellEdge.fill(zero);
        Flux_qtmvtAtCellEdge.fill(zero);
    
        // Les flux aux nodes/edge/faces
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            const auto& cell_to_node = cell_to_node_matrix[j];
    
            for (size_t l = 0; l < cell_to_node.size(); ++l) {
              // Etats conservatifs aux noeuds
              const double rhonode = StateAtNode[j][l][0];
              Rd Unode;
              for (size_t dim = 0; dim < Dimension; ++dim)
                Unode[dim] = StateAtNode[j][l][dim + 1] / rhonode;
              const double rhoEnode = StateAtNode[j][l][Dimension + 1];
              //
              const double Enode       = rhoEnode / rhonode;
              const double epsilonnode = Enode - .5 * dot(Unode, Unode);
              const Rd rhoUnode        = rhonode * Unode;
              const Rdxd rhoUtensUnode = tensorProduct(rhoUnode, Unode);
    
              const double Pressionnode = pression(rhonode, epsilonnode, gamma);
    
              const double rhoEnodePlusP = rhoEnode + Pressionnode;
    
              Rdxd rhoUtensUPlusPidnode(identity);
              rhoUtensUPlusPidnode *= Pressionnode;
              rhoUtensUPlusPidnode += rhoUtensUnode;
    
              Flux_rhoAtCellNode[j][l]    = rhoUnode;
              Flux_qtmvtAtCellNode[j][l]  = rhoUtensUPlusPidnode;
              Flux_totnrjAtCellNode[j][l] = rhoEnodePlusP * Unode;
            }
    
            const auto& cell_to_face = cell_to_face_matrix[j];
    
            for (size_t l = 0; l < cell_to_face.size(); ++l) {
              const double rhoface = StateAtFace[j][l][0];
              Rd Uface;
              for (size_t dim = 0; dim < Dimension; ++dim)
                Uface[dim] = StateAtFace[j][l][dim + 1] / rhoface;
              const double rhoEface = StateAtFace[j][l][Dimension + 1];
              //
              const double Eface       = rhoEface / rhoface;
              const double epsilonface = Eface - .5 * dot(Uface, Uface);
              const Rd rhoUface        = rhoface * Uface;
              const Rdxd rhoUtensUface = tensorProduct(rhoUface, Uface);
    
              const double Pressionface = pression(rhoface, epsilonface, gamma);
    
              const double rhoEfacePlusP = rhoEface + Pressionface;
    
              Rdxd rhoUtensUPlusPidface(identity);
              rhoUtensUPlusPidface *= Pressionface;
              rhoUtensUPlusPidface += rhoUtensUface;
    
              Flux_rhoAtCellFace[j][l]    = rhoUface;
              Flux_qtmvtAtCellFace[j][l]  = rhoUtensUPlusPidface;
              Flux_totnrjAtCellFace[j][l] = rhoEfacePlusP * Uface;
            }
    
            if constexpr (Dimension == 3) {
              const auto& cell_to_edge = cell_to_edge_matrix[j];
    
              for (size_t l = 0; l < cell_to_edge.size(); ++l) {
                const double rhoedge = StateAtEdge[j][l][0];
                Rd Uedge;
                for (size_t dim = 0; dim < Dimension; ++dim)
                  Uedge[dim] = StateAtEdge[j][l][dim + 1] / rhoedge;
                const double rhoEedge = StateAtEdge[j][l][Dimension + 1];
                //
                const double Eedge       = rhoEedge / rhoedge;
                const double epsilonedge = Eedge - .5 * dot(Uedge, Uedge);
                const Rd rhoUedge        = rhoedge * Uedge;
                const Rdxd rhoUtensUedge = tensorProduct(rhoUedge, Uedge);
    
                const double Pressionedge = pression(rhoedge, epsilonedge, gamma);
    
                const double rhoEedgePlusP = rhoEedge + Pressionedge;
    
                Rdxd rhoUtensUPlusPidedge(identity);
                rhoUtensUPlusPidedge *= Pressionedge;
                rhoUtensUPlusPidedge += rhoUtensUedge;
    
                Flux_rhoAtCellEdge[j][l]    = rhoUedge;
                Flux_qtmvtAtCellEdge[j][l]  = rhoUtensUPlusPidedge;
                Flux_totnrjAtCellEdge[j][l] = rhoEedgePlusP * Uedge;
              }
            }
          });
    
        // parallel_for(
        //   p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
        //     Flux_totnrjAtCellNode[j] = Flux_totnrjAtCellEdge[j] = Flux_totnrjAtCellFace[j] = Flux_totnrj[j];
        //   });
    
        MeshData<MeshType>& mesh_data = MeshDataManager::instance().getMeshData(*p_mesh);
    
        auto volumes_cell = mesh_data.Vj();
    
        // Calcul des matrices de viscosité aux node/edge/face
    
        const NodeValuePerCell<const Rd> Cjr = mesh_data.Cjr();
        const NodeValuePerCell<const Rd> njr = mesh_data.njr();
    
        const FaceValuePerCell<const Rd> Cjf = mesh_data.Cjf();
        const FaceValuePerCell<const Rd> njf = mesh_data.njf();
    
        const auto& node_to_cell_matrix               = p_mesh->connectivity().nodeToCellMatrix();
        const auto& node_local_numbers_in_their_cells = p_mesh->connectivity().nodeLocalNumbersInTheirCells();
    
        const auto& face_to_cell_matrix               = p_mesh->connectivity().faceToCellMatrix();
        const auto& face_local_numbers_in_their_cells = p_mesh->connectivity().faceLocalNumbersInTheirCells();
    
        // We compute Gjr, Gjf
    
        NodeValuePerCell<Rp> Gjr{p_mesh->connectivity()};
        Gjr.fill(zero);
        EdgeValuePerCell<Rp> Gje{p_mesh->connectivity()};
        Gje.fill(zero);
        FaceValuePerCell<Rp> Gjf{p_mesh->connectivity()};
        Gjf.fill(zero);
    
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            const auto& cell_to_node = cell_to_node_matrix[j];
    
            for (size_t l = 0; l < cell_to_node.size(); ++l) {
              const NodeId& node                         = cell_to_node[l];
              const auto& node_to_cell                   = node_to_cell_matrix[node];
              const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(node);
    
              const Rd& Cjr_loc = Cjr(j, l);
    
              for (size_t k = 0; k < node_to_cell.size(); ++k) {
                const CellId K    = node_to_cell[k];
                const size_t R    = node_local_number_in_its_cells[k];
                const Rd& Ckr_loc = Cjr(K, R);
    
                // Une moyenne entre les etats jk
    
                Rd uNode     = .5 * (u_n[j] + u_n[K]);
                double cNode = .5 * (c_n[j] + c_n[K]);
    
                // Viscosity j k
                Rpxp ViscosityMatrixJK(identity);
                const double MaxmaxabsVpNormjk =
                  std::max(toolsCompositeSolver::EvaluateMaxEigenValueTimesNormalLengthInGivenDirection(uNode, cNode,
                                                                                                        Cjr_loc),
                           toolsCompositeSolver::EvaluateMaxEigenValueTimesNormalLengthInGivenDirection(uNode, cNode,
                                                                                                        Ckr_loc));
    
                ViscosityMatrixJK *= MaxmaxabsVpNormjk;
                const Rd& u_Cjr = Flux_qtmvtAtCellNode[K][R] * Cjr_loc;   // Flux_qtmvt[K] * Cjr_loc;
    
                const Rp& statediff = StateAtNode[j][l] - StateAtNode[K][R];   // State[j] - State[K];
                const Rp& diff      = ViscosityMatrixJK * statediff;
    
                Gjr[j][l][0] += dot(Flux_rhoAtCellNode[K][R], Cjr_loc);   // dot(Flux_rho[K], Cjr_loc);
                for (size_t d = 0; d < Dimension; ++d)
                  Gjr[j][l][1 + d] += u_Cjr[d];
                Gjr[j][l][1 + Dimension] += dot(Flux_totnrjAtCellNode[K][R], Cjr_loc);   // dot(Flux_totnrj[K], Cjr_loc);
    
                Gjr[j][l] += diff;
              }
    
              Gjr[j][l] *= 1. / node_to_cell.size();
            }
          });
    
        synchronize(Gjr);
        if (checkLocalConservation) {
          auto is_boundary_node = p_mesh->connectivity().isBoundaryNode();
    
          NodeValue<double> MaxErrorConservationNode(p_mesh->connectivity());
          MaxErrorConservationNode.fill(0.);
          // double MaxErrorConservationNode = 0;
          parallel_for(
            p_mesh->numberOfNodes(), PUGS_LAMBDA(NodeId l) {
              const auto& node_to_cell                   = node_to_cell_matrix[l];
              const auto& node_local_number_in_its_cells = node_local_numbers_in_their_cells.itemArray(l);
    
              if (not is_boundary_node[l]) {
                Rp SumGjr(zero);
                double maxGjrAbs = 0;
                for (size_t k = 0; k < node_to_cell.size(); ++k) {
                  const CellId K       = node_to_cell[k];
                  const unsigned int R = node_local_number_in_its_cells[k];
                  SumGjr += Gjr[K][R];
                  maxGjrAbs = std::max(maxGjrAbs, l2Norm(Gjr[K][R]));
                }
                // MaxErrorConservationNode = std::max(MaxErrorConservationNode, l2Norm(SumGjr));
                MaxErrorConservationNode[l] = l2Norm(SumGjr) / maxGjrAbs;
              }
            });
          std::cout << " Max Error Node " << max(MaxErrorConservationNode) << "\n";
        }
        //
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            // Edge
            const auto& cell_to_face = cell_to_face_matrix[j];
    
            for (size_t l = 0; l < cell_to_face.size(); ++l) {
              const FaceId& face                         = cell_to_face[l];
              const auto& face_to_cell                   = face_to_cell_matrix[face];
              const auto& face_local_number_in_its_cells = face_local_numbers_in_their_cells.itemArray(face);
    
              const Rd& Cjf_loc = Cjf(j, l);
    
              CellId K=face_to_cell[0];
    	        unsigned int R =face_local_number_in_its_cells[0];
    
              if (face_to_cell.size()==1)
              {
                K=j;
                R=l;
              }
              else
              {
                const CellId K1       = face_to_cell[0];
      	        const CellId K2       = face_to_cell[1];
    
                if (j==K1)
                {
                  K = K2;
                  R = face_local_number_in_its_cells[1];
                }
              }
    
              const double rhoj = StateAtFace[j][l][0];
              const double rhoK = StateAtFace[K][R][0];
              Rd Uj;
              Rd UK;
              for (size_t dim = 0; dim < Dimension; ++dim){
                Uj[dim] = StateAtFace[j][l][dim + 1] / rhoj;
                UK[dim] = StateAtFace[K][R][dim + 1] / rhoK;
              }
              const double uL = Uj[0];
              const double uR = UK[0];
              const double rhoEj = StateAtFace[j][l][Dimension + 1];
              const double rhoEK = StateAtFace[K][R][Dimension + 1];
              const double Ej        = rhoEj / rhoj;
              const double EK        = rhoEK / rhoK;
              const double epsilonj  = Ej - .5 * dot(Uj, Uj);
              const double epsilonK  = EK - .5 * dot(UK, UK);
              const double Pressionj = pression(rhoj, epsilonj, gamma);
              const double PressionK = pression(rhoK, epsilonK, gamma);
              
              const std::pair<double, double> MinMaxVpNormj = toolsCompositeSolver::EvaluateMinMaxEigenValueTimesNormalLengthInGivenDirection(u_n[j], c_n[j], Cjf_loc);
              const std::pair<double, double> MinMaxVpNormk = toolsCompositeSolver::EvaluateMinMaxEigenValueTimesNormalLengthInGivenDirection(u_n[K], c_n[K], Cjf_loc); 
              const double MinVpNormjk = std::min(MinMaxVpNormj.first, MinMaxVpNormk.first) / l2Norm(Cjf_loc);   // SL
              const double MaxVpNormjk = std::max(MinMaxVpNormj.second, MinMaxVpNormk.second) / l2Norm(Cjf_loc); //  SR
    
              const double diffP = PressionK - Pressionj;
              const double diffVelocityj = MinVpNormjk - uL;
              const double diffVelocityK = MaxVpNormjk - uR;
              const double SC = (diffP + rhoj * uL * diffVelocityj - rhoK * uR * diffVelocityK)/(rhoj * diffVelocityj - rhoK * diffVelocityK); // SC
    
              if (MinVpNormjk >= 0 ){ // SL ≥ 0
                const Rd& uj_Cjf = Flux_qtmvtAtCellFace[j][l] * Cjf_loc;   // Flux_qtmvt[j] * Cjf_loc;
    
                Gjf[j][l][0] = dot(Flux_rhoAtCellFace[j][l], Cjf_loc);   // dot(Flux_roh[j] , Cjf_loc)
                for (size_t d = 0; d < Dimension; ++d)
                  Gjf[j][l][1 + d] = uj_Cjf[d];
                Gjf[j][l][1 + Dimension] = dot(Flux_totnrjAtCellFace[j][l], Cjf_loc);    // dot(Flux_totnrj[K] , Cjf_loc)
              }
              else{
                if (MaxVpNormjk <= 0 ){ // SR ≤ 0
                  const Rd& uk_Cjf = Flux_qtmvtAtCellFace[K][R] * Cjf_loc;   // Flux_qtmvt[K] * Cjf_loc;
                  Gjf[j][l][0] = dot(Flux_rhoAtCellFace[K][R], Cjf_loc);   // dot(Flux_roh[K] , Cjf_loc)
                  for (size_t d = 0; d < Dimension; ++d)
                    Gjf[j][l][1 + d] = uk_Cjf[d];
                  Gjf[j][l][1 + Dimension] = dot(Flux_totnrjAtCellFace[K][R], Cjf_loc);    // dot(Flux_totnrj[K] , Cjf_loc)
                }
                else{
                  if (SC >= 0){ // SL ≤ 0 ≤ SC
                    const Rd& uj_Cjf = Flux_qtmvtAtCellFace[j][l] * Cjf_loc;   // Flux_qtmvt[j] * Cjf_loc;
        
                    Gjf[j][l][0] = dot(Flux_rhoAtCellFace[j][l], Cjf_loc);   // dot(Flux_roh[j] , Cjf_loc)
                    for (size_t d = 0; d < Dimension; ++d)
                      Gjf[j][l][1 + d] = uj_Cjf[d];
                    Gjf[j][l][1 + Dimension] = dot(Flux_totnrjAtCellFace[j][l], Cjf_loc);    // dot(Flux_totnrj[K] , Cjf_loc)
        
                    Rp DL;
                    DL[0] = 1;
                    DL[1] = SC;
                    for (size_t d = 2; d < (Dimension + 1); ++d){
                      DL[d] = Uj[d-1];
                    }
                    DL[Dimension + 1] = Ej + rhoj * (SC - uL) * (SC + (Pressionj / (rhoj * diffVelocityj)));
                      
                    const Rp UCL = rhoj * (diffVelocityj / (MinVpNormjk - SC)) * DL;
                    const Rp diffStates = MinVpNormjk * l2Norm(Cjf_loc) * (UCL - StateAtFace[j][l]);
                    Gjf[j][l] += diffStates;
                  }
                  else{
                    // SC ≤ 0 ≤ SR
                    const Rd& uk_Cjf = Flux_qtmvtAtCellFace[K][R] * Cjf_loc;   // Flux_qtmvt[K] * Cjf_loc;
                    Gjf[j][l][0] = dot(Flux_rhoAtCellFace[K][R], Cjf_loc);   // dot(Flux_roh[K] , Cjf_loc)
                    for (size_t d = 0; d < Dimension; ++d)
                      Gjf[j][l][1 + d] = uk_Cjf[d];
                    Gjf[j][l][1 + Dimension] = dot(Flux_totnrjAtCellFace[K][R], Cjf_loc);    // dot(Flux_totnrj[K] , Cjf_loc)
        
                    Rp DR;
                    DR[0] = 1;
                    DR[1] = SC;
                    for (size_t d = 2; d < (Dimension + 1); ++d){
                      DR[d] = UK[d-1];            
                    }
                    DR[Dimension + 1] = EK + rhoK * (SC - uR) * (SC + (PressionK / (rhoK * diffVelocityK)));
                        
                    const Rp UCR = rhoK * (diffVelocityK / (MaxVpNormjk - SC)) * DR;
                    const Rp diffStates = MaxVpNormjk * l2Norm(Cjf_loc) * (UCR - StateAtFace[K][R]);
                    Gjf[j][l] += diffStates;
                  }
                }
              }
            }
          });
        synchronize(Gjf);
    
        if (checkLocalConservation) {
          auto is_boundary_face = p_mesh->connectivity().isBoundaryFace();
    
          FaceValue<double> MaxErrorConservationFace(p_mesh->connectivity());
          MaxErrorConservationFace.fill(0.);
    
          parallel_for(
            p_mesh->numberOfFaces(), PUGS_LAMBDA(FaceId l) {
              const auto& face_to_cell                   = face_to_cell_matrix[l];
              const auto& face_local_number_in_its_cells = face_local_numbers_in_their_cells.itemArray(l);
    
              if (not is_boundary_face[l]) {
                Rp SumGjf(zero);
                double maxGjrAbs = 0;
                for (size_t k = 0; k < face_to_cell.size(); ++k) {
                  const CellId K       = face_to_cell[k];
                  const unsigned int R = face_local_number_in_its_cells[k];
                  SumGjf += Gjf[K][R];
                  maxGjrAbs = std::max(maxGjrAbs, l2Norm(Gjf[K][R]));
                }
                MaxErrorConservationFace[l] = l2Norm(SumGjf) / maxGjrAbs;
                // MaxErrorConservationFace   = std::max(MaxErrorConservationFace, l2Norm(SumGjf));
              }
            });
          std::cout << " Max Error Face " << max(MaxErrorConservationFace) << "\n";
        }
    
        if constexpr (Dimension == 3) {
          const auto& edge_to_cell_matrix               = p_mesh->connectivity().edgeToCellMatrix();
          const auto& edge_local_numbers_in_their_cells = p_mesh->connectivity().edgeLocalNumbersInTheirCells();
    
          const EdgeValuePerCell<const Rd> Cje = mesh_data.Cje();
          const EdgeValuePerCell<const Rd> nje = mesh_data.nje();
    
          parallel_for(
            p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
              // Edge
              const auto& cell_to_edge = cell_to_edge_matrix[j];
    
              for (size_t l = 0; l < cell_to_edge.size(); ++l) {
                const EdgeId& edge                         = cell_to_edge[l];
                const auto& edge_to_cell                   = edge_to_cell_matrix[edge];
                const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(edge);
    
                const Rd& Cje_loc = Cje(j, l);
    
                for (size_t k = 0; k < edge_to_cell.size(); ++k) {
                  const CellId K = edge_to_cell[k];
                  const size_t R = edge_local_number_in_its_cells[k];
    
                  const Rd& Cke_loc = Cje(K, R);
    
                  // Une moyenne entre les etats jk
    
                  Rd uEdge     = .5 * (u_n[j] + u_n[K]);
                  double cEdge = .5 * (c_n[j] + c_n[K]);
    
                  // Viscosity j k
                  Rpxp ViscosityMatrixJK(identity);
                  const double MaxmaxabsVpNormjk =
                    std::max(toolsCompositeSolver::EvaluateMaxEigenValueTimesNormalLengthInGivenDirection(uEdge, cEdge,
                                                                                                          Cje_loc),
                             toolsCompositeSolver::EvaluateMaxEigenValueTimesNormalLengthInGivenDirection(uEdge, cEdge,
                                                                                                          Cke_loc));
    
                  ViscosityMatrixJK *= MaxmaxabsVpNormjk;
    
                  const Rd& u_Cje = Flux_qtmvtAtCellEdge[K][R] * Cje_loc;   // Flux_qtmvt[K] * Cje_loc;
    
                  const Rp& statediff = StateAtEdge[j][l] - StateAtEdge[K][R];   // State[j] - State[K];
                  const Rp& diff      = ViscosityMatrixJK * statediff;
    
                  Gje[j][l][0] += dot(Flux_rhoAtCellEdge[K][R], Cje_loc);   //  dot(Flux_rho[K], Cje_loc);
                  for (size_t d = 0; d < Dimension; ++d)
                    Gje[j][l][1 + d] += u_Cje[d];
                  Gje[j][l][1 + Dimension] += dot(Flux_totnrjAtCellEdge[K][R], Cje_loc);   // dot(Flux_totnrj[K], Cje_loc);
    
                  Gje[j][l] += diff;
                }
    
                Gje[j][l] *= 1. / edge_to_cell.size();
              }
            });
          synchronize(Gje);
    
          if (checkLocalConservation) {
            auto is_boundary_edge = p_mesh->connectivity().isBoundaryEdge();
    
            EdgeValue<double> MaxErrorConservationEdge(p_mesh->connectivity());
            MaxErrorConservationEdge.fill(0.);
            //  double MaxErrorConservationEdge = 0;
            parallel_for(
              p_mesh->numberOfEdges(), PUGS_LAMBDA(EdgeId l) {
                const auto& edge_to_cell                   = edge_to_cell_matrix[l];
                const auto& edge_local_number_in_its_cells = edge_local_numbers_in_their_cells.itemArray(l);
    
                if (not is_boundary_edge[l]) {
                  Rp SumGje(zero);
                  double maxGjrAbs = 0;
                  for (size_t k = 0; k < edge_to_cell.size(); ++k) {
                    const CellId K       = edge_to_cell[k];
                    const unsigned int R = edge_local_number_in_its_cells[k];
                    SumGje += Gje[K][R];
                    maxGjrAbs = std::max(maxGjrAbs, l2Norm(Gje[K][R]));
                  }
                  // MaxErrorConservationEdge = std::max(MaxErrorConservationEdge, l2Norm(SumGje));
                  MaxErrorConservationEdge[l] = l2Norm(SumGje) / maxGjrAbs;
                }
              });
            std::cout << " Max Error Edge " << max(MaxErrorConservationEdge) << "\n";
          }
        }   // dim 3
    
        // Pour les assemblages
        double theta = 2. / 3.;   //.5; 2. / 3.
        double eta   = 1. / 6.;   //.2; 1. / 6.
        if constexpr (Dimension == 2) {
          eta = 0;
        }
        // else{
        // theta = 1. / 3.;
        // eta   = 1. / 3.;
        // theta = .5;
        // eta   = 0;
        //}
        //
        parallel_for(
          p_mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
            const auto& cell_to_node = cell_to_node_matrix[j];
    
            Rp SumFluxesNode(zero);
    
            for (size_t l = 0; l < cell_to_node.size(); ++l) {
              SumFluxesNode += Gjr[j][l];
            }
            // SumFluxesNode *= (1 - theta);
    
            const auto& cell_to_edge = cell_to_edge_matrix[j];
            Rp SumFluxesEdge(zero);
    
            for (size_t l = 0; l < cell_to_edge.size(); ++l) {
              SumFluxesEdge += Gje[j][l];
            }
    
            const auto& cell_to_face = cell_to_face_matrix[j];
            Rp SumFluxesFace(zero);
    
            for (size_t l = 0; l < cell_to_face.size(); ++l) {
              SumFluxesFace += Gjf[j][l];
            }
            // SumFluxesEdge *= (theta);
    
            const Rp SumFluxes = (1 - theta - eta) * SumFluxesNode + eta * SumFluxesEdge + theta * SumFluxesFace;
    
            State[j] -= dt / volumes_cell[j] * SumFluxes;
    
            rho[j] = State[j][0];
            for (size_t d = 0; d < Dimension; ++d)
              u[j][d] = State[j][1 + d] / rho[j];
            E[j] = State[j][1 + Dimension] / rho[j];
          });
    
        return std::make_tuple(std::make_shared<const DiscreteFunctionVariant>(rho),
                               std::make_shared<const DiscreteFunctionVariant>(u),
                               std::make_shared<const DiscreteFunctionVariant>(E));
      }
    
      HybridHLLcRusanovEulerianCompositeSolver_v2()  = default;
      ~HybridHLLcRusanovEulerianCompositeSolver_v2() = default;
    };
    
    template <MeshConcept MeshType>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>::WallBoundaryCondition
    {
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<2>>::WallBoundaryCondition
    {
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
      // const MeshFlatNodeBoundary<MeshType> m_mesh_flat_node_boundary;
      // const MeshFlatFaceBoundary<MeshType> m_mesh_flat_face_boundary;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      WallBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary, const MeshFaceBoundary& mesh_face_boundary)
        : m_mesh_node_boundary(mesh_node_boundary), m_mesh_face_boundary(mesh_face_boundary)
      {
        ;
      }
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<3>>::WallBoundaryCondition
    {
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshEdgeBoundary m_mesh_edge_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
      size_t
      numberOfEdges() const
      {
        return m_mesh_edge_boundary.edgeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const EdgeId>&
      edgeList() const
      {
        return m_mesh_edge_boundary.edgeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      WallBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary,
                            const MeshEdgeBoundary& mesh_edge_boundary,
                            const MeshFaceBoundary& mesh_face_boundary)
        : m_mesh_node_boundary(mesh_node_boundary),
    
          m_mesh_edge_boundary(mesh_edge_boundary),
    
          m_mesh_face_boundary(mesh_face_boundary)
      {
        ;
      }
    };
    
    template <MeshConcept MeshType>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>::NeumannflatBoundaryCondition
    {
    };
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<2>>::NeumannflatBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshFlatNodeBoundary<MeshType> m_mesh_flat_node_boundary;
      const MeshFlatFaceBoundary<MeshType> m_mesh_flat_face_boundary;
    
     public:
      const Rd&
      outgoingNormal() const
      {
        return m_mesh_flat_node_boundary.outgoingNormal();
      }
    
      size_t
      numberOfNodes() const
      {
        return m_mesh_flat_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_flat_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_flat_node_boundary.nodeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_flat_face_boundary.faceList();
      }
    
      NeumannflatBoundaryCondition(const MeshFlatNodeBoundary<MeshType>& mesh_flat_node_boundary,
                                   const MeshFlatFaceBoundary<MeshType>& mesh_flat_face_boundary)
        : m_mesh_flat_node_boundary(mesh_flat_node_boundary), m_mesh_flat_face_boundary(mesh_flat_face_boundary)
      {
        ;
      }
    
      ~NeumannflatBoundaryCondition() = default;
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<3>>::NeumannflatBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshFlatNodeBoundary<MeshType> m_mesh_flat_node_boundary;
      const MeshFlatEdgeBoundary<MeshType> m_mesh_flat_edge_boundary;
      const MeshFlatFaceBoundary<MeshType> m_mesh_flat_face_boundary;
    
     public:
      const Rd&
      outgoingNormal() const
      {
        return m_mesh_flat_node_boundary.outgoingNormal();
      }
    
      size_t
      numberOfNodes() const
      {
        return m_mesh_flat_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfEdges() const
      {
        return m_mesh_flat_edge_boundary.edgeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_flat_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_flat_node_boundary.nodeList();
      }
    
      const Array<const EdgeId>&
      edgeList() const
      {
        return m_mesh_flat_edge_boundary.edgeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_flat_face_boundary.faceList();
      }
    
      NeumannflatBoundaryCondition(const MeshFlatNodeBoundary<MeshType>& mesh_flat_node_boundary,
                                   const MeshFlatEdgeBoundary<MeshType>& mesh_flat_edge_boundary,
                                   const MeshFlatFaceBoundary<MeshType>& mesh_flat_face_boundary)
        : m_mesh_flat_node_boundary(mesh_flat_node_boundary),
          m_mesh_flat_edge_boundary(mesh_flat_edge_boundary),
          m_mesh_flat_face_boundary(mesh_flat_face_boundary)
      {
        ;
      }
    
      ~NeumannflatBoundaryCondition() = default;
    };
    
    template <MeshConcept MeshType>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>::SymmetryBoundaryCondition
    {
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<2>>::SymmetryBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshFlatNodeBoundary<MeshType> m_mesh_flat_node_boundary;
      const MeshFlatFaceBoundary<MeshType> m_mesh_flat_face_boundary;
    
     public:
      const Rd&
      outgoingNormal() const
      {
        return m_mesh_flat_node_boundary.outgoingNormal();
      }
    
      size_t
      numberOfNodes() const
      {
        return m_mesh_flat_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_flat_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_flat_node_boundary.nodeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_flat_face_boundary.faceList();
      }
    
      SymmetryBoundaryCondition(const MeshFlatNodeBoundary<MeshType>& mesh_flat_node_boundary,
                                const MeshFlatFaceBoundary<MeshType>& mesh_flat_face_boundary)
        : m_mesh_flat_node_boundary(mesh_flat_node_boundary), m_mesh_flat_face_boundary(mesh_flat_face_boundary)
      {
        ;
      }
    
      ~SymmetryBoundaryCondition() = default;
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<3>>::SymmetryBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshFlatNodeBoundary<MeshType> m_mesh_flat_node_boundary;
      const MeshFlatEdgeBoundary<MeshType> m_mesh_flat_edge_boundary;
      const MeshFlatFaceBoundary<MeshType> m_mesh_flat_face_boundary;
    
     public:
      const Rd&
      outgoingNormal() const
      {
        return m_mesh_flat_node_boundary.outgoingNormal();
      }
    
      size_t
      numberOfNodes() const
      {
        return m_mesh_flat_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfEdges() const
      {
        return m_mesh_flat_edge_boundary.edgeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_flat_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_flat_node_boundary.nodeList();
      }
    
      const Array<const EdgeId>&
      edgeList() const
      {
        return m_mesh_flat_edge_boundary.edgeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_flat_face_boundary.faceList();
      }
    
      SymmetryBoundaryCondition(const MeshFlatNodeBoundary<MeshType>& mesh_flat_node_boundary,
                                const MeshFlatEdgeBoundary<MeshType>& mesh_flat_edge_boundary,
                                const MeshFlatFaceBoundary<MeshType>& mesh_flat_face_boundary)
        : m_mesh_flat_node_boundary(mesh_flat_node_boundary),
          m_mesh_flat_edge_boundary(mesh_flat_edge_boundary),
          m_mesh_flat_face_boundary(mesh_flat_face_boundary)
      {
        ;
      }
    
      ~SymmetryBoundaryCondition() = default;
    };
    
    template <MeshConcept MeshType>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>::InflowListBoundaryCondition
    {
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<2>>::InflowListBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
      const Table<const double> m_node_array_list;
      const Table<const double> m_face_array_list;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      const Table<const double>&
      nodeArrayList() const
      {
        return m_node_array_list;
      }
    
      const Table<const double>&
      faceArrayList() const
      {
        return m_face_array_list;
      }
    
      InflowListBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary,
                                  const MeshFaceBoundary& mesh_face_boundary,
                                  const Table<const double>& node_array_list,
                                  const Table<const double>& face_array_list)
        : m_mesh_node_boundary(mesh_node_boundary),
          m_mesh_face_boundary(mesh_face_boundary),
          m_node_array_list(node_array_list),
          m_face_array_list(face_array_list)
      {
        ;
      }
    
      ~InflowListBoundaryCondition() = default;
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<3>>::InflowListBoundaryCondition
    {
     public:
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshEdgeBoundary m_mesh_edge_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
      const Table<const double> m_node_array_list;
      const Table<const double> m_edge_array_list;
      const Table<const double> m_face_array_list;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfEdges() const
      {
        return m_mesh_edge_boundary.edgeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const EdgeId>&
      edgeList() const
      {
        return m_mesh_edge_boundary.edgeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      const Table<const double>&
      nodeArrayList() const
      {
        return m_node_array_list;
      }
    
      const Table<const double>&
      edgeArrayList() const
      {
        return m_edge_array_list;
      }
    
      const Table<const double>&
      faceArrayList() const
      {
        return m_face_array_list;
      }
    
      InflowListBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary,
                                  const MeshEdgeBoundary& mesh_edge_boundary,
                                  const MeshFaceBoundary& mesh_face_boundary,
                                  const Table<const double>& node_array_list,
                                  const Table<const double>& edge_array_list,
                                  const Table<const double>& face_array_list)
        : m_mesh_node_boundary(mesh_node_boundary),
          m_mesh_edge_boundary(mesh_edge_boundary),
          m_mesh_face_boundary(mesh_face_boundary),
          m_node_array_list(node_array_list),
          m_edge_array_list(edge_array_list),
          m_face_array_list(face_array_list)
      {
        ;
      }
    
      ~InflowListBoundaryCondition() = default;
    };
    
    template <MeshConcept MeshType>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>::OutflowBoundaryCondition
    {
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<2>>::OutflowBoundaryCondition
    {
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      OutflowBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary, const MeshFaceBoundary& mesh_face_boundary)
        : m_mesh_node_boundary(mesh_node_boundary), m_mesh_face_boundary(mesh_face_boundary)
      {
        ;
      }
    };
    
    template <>
    class HybridHLLcRusanovEulerianCompositeSolver_v2<Mesh<3>>::OutflowBoundaryCondition
    {
      using Rd = TinyVector<Dimension, double>;
    
     private:
      const MeshNodeBoundary m_mesh_node_boundary;
      const MeshEdgeBoundary m_mesh_edge_boundary;
      const MeshFaceBoundary m_mesh_face_boundary;
    
     public:
      size_t
      numberOfNodes() const
      {
        return m_mesh_node_boundary.nodeList().size();
      }
      size_t
      numberOfEdges() const
      {
        return m_mesh_edge_boundary.edgeList().size();
      }
    
      size_t
      numberOfFaces() const
      {
        return m_mesh_face_boundary.faceList().size();
      }
    
      const Array<const NodeId>&
      nodeList() const
      {
        return m_mesh_node_boundary.nodeList();
      }
    
      const Array<const EdgeId>&
      edgeList() const
      {
        return m_mesh_edge_boundary.edgeList();
      }
    
      const Array<const FaceId>&
      faceList() const
      {
        return m_mesh_face_boundary.faceList();
      }
    
      OutflowBoundaryCondition(const MeshNodeBoundary& mesh_node_boundary,
                               const MeshEdgeBoundary& mesh_edge_boundary,
                               const MeshFaceBoundary& mesh_face_boundary)
        : m_mesh_node_boundary(mesh_node_boundary),
    
          m_mesh_edge_boundary(mesh_edge_boundary),
    
          m_mesh_face_boundary(mesh_face_boundary)
      {
        ;
      }
    };
    
    std::tuple<std::shared_ptr<const DiscreteFunctionVariant>,
               std::shared_ptr<const DiscreteFunctionVariant>,
               std::shared_ptr<const DiscreteFunctionVariant>>
    hybridHLLcRusanovEulerianCompositeSolver_v2(
      const std::shared_ptr<const DiscreteFunctionVariant>& rho_v,
      const std::shared_ptr<const DiscreteFunctionVariant>& u_v,
      const std::shared_ptr<const DiscreteFunctionVariant>& E_v,
      const double& gamma,
      const std::shared_ptr<const DiscreteFunctionVariant>& c_v,
      const std::shared_ptr<const DiscreteFunctionVariant>& p_v,
      //  const size_t& degree,
      const std::vector<std::shared_ptr<const IBoundaryConditionDescriptor>>& bc_descriptor_list,
      const double& dt,
      const bool check)
    {
      std::shared_ptr mesh_v = getCommonMesh({rho_v, u_v, E_v, c_v, p_v});
      if (not mesh_v) {
        throw NormalError("discrete functions are not defined on the same mesh");
      }
    
      if (not checkDiscretizationType({rho_v, u_v, E_v}, DiscreteFunctionType::P0)) {
        throw NormalError("acoustic solver expects P0 functions");
      }
    
      return std::visit(
        PUGS_LAMBDA(auto&& p_mesh)
          ->std::tuple<std::shared_ptr<const DiscreteFunctionVariant>, std::shared_ptr<const DiscreteFunctionVariant>,
                       std::shared_ptr<const DiscreteFunctionVariant>> {
            using MeshType                    = mesh_type_t<decltype(p_mesh)>;
            static constexpr size_t Dimension = MeshType::Dimension;
            using Rd                          = TinyVector<Dimension>;
    
            if constexpr (Dimension == 1) {
              throw NormalError("Hybrid HLLc/Rusanov EulerianCompositeSolver v2 is not available in 1D");
            } else {
              if constexpr (is_polygonal_mesh_v<MeshType>) {
                return HybridHLLcRusanovEulerianCompositeSolver_v2<MeshType>{}
                  .solve(p_mesh, rho_v->get<DiscreteFunctionP0<const double>>(), u_v->get<DiscreteFunctionP0<const Rd>>(),
                         E_v->get<DiscreteFunctionP0<const double>>(), gamma, c_v->get<DiscreteFunctionP0<const double>>(),
                         p_v->get<DiscreteFunctionP0<const double>>(), bc_descriptor_list, dt, check);
              } else {
                throw NormalError("Hybrid HLLc/Rusanov EulerianCompositeSolver v2 is only defined on polygonal meshes");
              }
            }
          },
        mesh_v->variant());
    }