spatial_operator_base.h

/*  ______________________________________________________________________
 *
 *  ExaDG - High-Order Discontinuous Galerkin for the Exa-Scale
 *
 *  Copyright (C) 2021 by the ExaDG authors
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <https://www.gnu.org/licenses/>.
 *  ______________________________________________________________________
 */
 
#ifndef INCLUDE_EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_SPATIAL_OPERATOR_BASE_H_
#define INCLUDE_EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_SPATIAL_OPERATOR_BASE_H_
 
// deal.II
#include <deal.II/fe/fe_dgq.h>
#include <deal.II/fe/fe_raviart_thomas.h>
#include <deal.II/fe/fe_simplex_p.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/lac/la_parallel_block_vector.h>
#include <deal.II/lac/la_parallel_vector.h>
 
 
// ExaDG
#include <exadg/grid/grid.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/calculators/streamfunction_calculator_rhs_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/generalized_newtonian_model.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/convective_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/divergence_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/gradient_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/momentum_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/projection_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/rhs_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/operators/viscous_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/turbulence_model.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/viscosity_model_base.h>
#include <exadg/incompressible_navier_stokes/user_interface/boundary_descriptor.h>
#include <exadg/incompressible_navier_stokes/user_interface/field_functions.h>
#include <exadg/incompressible_navier_stokes/user_interface/parameters.h>
#include <exadg/matrix_free/matrix_free_data.h>
#include <exadg/operators/inverse_mass_operator.h>
#include <exadg/operators/mass_operator.h>
#include <exadg/operators/navier_stokes_calculators.h>
#include <exadg/poisson/preconditioners/multigrid_preconditioner.h>
#include <exadg/poisson/spatial_discretization/laplace_operator.h>
#include <exadg/solvers_and_preconditioners/preconditioners/preconditioner_base.h>
#include <exadg/time_integration/interpolate.h>
 
namespace ExaDG
{
namespace IncNS
{
template<int dim, typename Number>
class SpatialOperatorBase;
 
template<int dim, typename Number>
class SpatialOperatorBase : public dealii::Subscriptor
{
protected:
  typedef dealii::LinearAlgebra::distributed::Vector<Number>      VectorType;
  typedef dealii::LinearAlgebra::distributed::BlockVector<Number> BlockVectorType;
 
  typedef SpatialOperatorBase<dim, Number> This;
 
  typedef dealii::VectorizedArray<Number>                         scalar;
  typedef dealii::Tensor<1, dim, dealii::VectorizedArray<Number>> vector;
  typedef dealii::Tensor<2, dim, dealii::VectorizedArray<Number>> tensor;
 
  typedef std::pair<unsigned int, unsigned int> Range;
 
  typedef FaceIntegrator<dim, dim, Number> FaceIntegratorU;
  typedef FaceIntegrator<dim, 1, Number>   FaceIntegratorP;
 
  typedef typename Poisson::MultigridPreconditioner<dim, Number, 1> MultigridPoisson;
 
public:
  /*
   * Constructor.
   */
  SpatialOperatorBase(std::shared_ptr<Grid<dim> const>                      grid,
                      std::shared_ptr<dealii::Mapping<dim> const>           mapping,
                      std::shared_ptr<MultigridMappings<dim, Number>> const multigrid_mappings,
                      std::shared_ptr<BoundaryDescriptor<dim> const>        boundary_descriptor,
                      std::shared_ptr<FieldFunctions<dim> const>            field_functions,
                      Parameters const &                                    parameters,
                      std::string const &                                   field,
                      MPI_Comm const &                                      mpi_comm);
 
  /*
   * Destructor.
   */
  virtual ~SpatialOperatorBase(){};
 
  void
  fill_matrix_free_data(MatrixFreeData<dim, Number> & matrix_free_data) const;

  void
  setup();

  void
  setup(std::shared_ptr<dealii::MatrixFree<dim, Number> const> matrix_free,
        std::shared_ptr<MatrixFreeData<dim, Number> const>     matrix_free_data,
        std::string const &                                    dof_index_temperature = "");
 
protected:
  /*
   * This function initializes operators, preconditioners, and solvers related to the solution of
   * (non-)linear systems of equation required for implicit formulations. It has to be extended
   * by derived classes if necessary.
   */
  virtual void
  setup_preconditioners_and_solvers()
  {
  }
 
private:
  virtual void
  setup_derived() = 0;
 
public:
  /*
   * Getters and setters.
   */
  dealii::MatrixFree<dim, Number> const &
  get_matrix_free() const;
 
  std::string
  get_dof_name_velocity() const;
 
  unsigned int
  get_dof_index_velocity() const;
 
  unsigned int
  get_dof_index_pressure() const;
 
  unsigned int
  get_quad_index_velocity_standard() const;
 
  unsigned int
  get_quad_index_pressure() const;
 
protected:
  unsigned int
  get_dof_index_velocity_scalar() const;
 
  unsigned int
  get_quad_index_velocity_overintegration() const;
 
  unsigned int
  get_quad_index_velocity_nodal_points() const;
 
  unsigned int
  get_quad_index_pressure_nodal_points() const;
 
  unsigned int
  get_quad_index_velocity_linearized() const;
 
public:
  std::shared_ptr<dealii::Mapping<dim> const>
  get_mapping() const;
 
  dealii::FiniteElement<dim> const &
  get_fe_u() const;
 
  dealii::FiniteElement<dim> const &
  get_fe_p() const;
 
  dealii::DoFHandler<dim> const &
  get_dof_handler_u() const;
 
  dealii::DoFHandler<dim> const &
  get_dof_handler_u_scalar() const;
 
  dealii::DoFHandler<dim> const &
  get_dof_handler_p() const;
 
  dealii::AffineConstraints<Number> const &
  get_constraint_p() const;
 
  dealii::AffineConstraints<Number> const &
  get_constraint_u() const;
 
  dealii::types::global_dof_index
  get_number_of_dofs() const;
 
  dealii::VectorizedArray<Number>
  get_viscosity_boundary_face(unsigned int const face, unsigned int const q) const;
 
  // Multiphysics coupling via "Cached" boundary conditions
  std::shared_ptr<ContainerInterfaceData<1, dim, double>>
  get_container_interface_data();
 
  void
  set_velocity_ptr(VectorType const & velocity) const;
 
  /*
   * Initialization of vectors.
   */
  void
  initialize_vector_velocity(VectorType & src) const;
 
  void
  initialize_vector_velocity_scalar(VectorType & src) const;
 
  void
  initialize_vector_pressure(VectorType & src) const;
 
  void
  initialize_block_vector_velocity_pressure(BlockVectorType & src) const;
 
  /*
   * Prescribe initial conditions using a specified analytical/initial solution function.
   */
  void
  prescribe_initial_conditions(VectorType & velocity,
                               VectorType & pressure,
                               double const time) const;
 
  /*
   * Interpolate given functions to the corresponding vectors.
   */
  void
  interpolate_functions(VectorType &                                   velocity,
                        std::shared_ptr<dealii::Function<dim>> const & f_velocity,
                        VectorType &                                   pressure,
                        std::shared_ptr<dealii::Function<dim>> const & f_pressure,
                        double const                                   time) const;
 
  /*
   * Interpolate analytical solution functions.
   */
  void
  interpolate_analytical_solution(VectorType & velocity,
                                  VectorType & pressure,
                                  double const time) const;
 
  // FSI: coupling fluid -> structure
  // fills a DoF-vector (velocity) with values of traction on fluid-structure interface
  void
  interpolate_stress_bc(VectorType &       stress,
                        VectorType const & velocity,
                        VectorType const & pressure) const;
 
  /*
   * Time step calculation.
   */
 
  /*
   * Calculate time step size according to maximum efficiency criterion
   */
  double
  calculate_time_step_max_efficiency(unsigned int const order_time_integrator) const;
 
  // global CFL criterion
  double
  calculate_time_step_cfl_global() const;
 
  // Calculate time step size according to local CFL criterion
  double
  calculate_time_step_cfl(VectorType const & velocity) const;
 
  // Calculate CFL numbers of cells
  void
  calculate_cfl_from_time_step(VectorType &       cfl,
                               VectorType const & velocity,
                               double const       time_step_size) const;
 
  /*
   * Returns characteristic element length for high-order elements / shape functions
   */
  double
  get_characteristic_element_length() const;
 
  /*
   * For certain setups and types of boundary conditions, the pressure field is only defined up to
   * an additive constant which originates from the fact that only the derivative of the pressure
   * appears in the incompressible Navier-Stokes equations. Examples of such a scenario are problems
   * where the velocity is prescribed on the whole boundary or periodic boundaries.
   */
 
  // This function can be used to query whether the pressure level is undefined.
  bool
  is_pressure_level_undefined() const;
 
  // This function adjust the pressure level, where different options are available to fix the
  // pressure level. The method selected by this function depends on the specified parameter.
  void
  adjust_pressure_level_if_undefined(VectorType & pressure, double const & time) const;
 
  /*
   *  Boussinesq approximation
   */
  void
  set_temperature(VectorType const & temperature);
 
  /*
   * Computation of derived quantities which is needed for postprocessing but some of them are also
   * needed, e.g., for special splitting-type time integration schemes.
   */
 
  // vorticity
  void
  compute_vorticity(VectorType & dst, VectorType const & src) const;
 
  // divergence
  void
  compute_divergence(VectorType & dst, VectorType const & src) const;
 
  // shear rate
  void
  compute_shear_rate(VectorType & dst, VectorType const & src) const;
 
  // velocity_magnitude
  void
  compute_velocity_magnitude(VectorType & dst, VectorType const & src) const;
 
  // vorticity_magnitude
  void
  compute_vorticity_magnitude(VectorType & dst, VectorType const & src) const;
 
  // streamfunction
  void
  compute_streamfunction(VectorType & dst, VectorType const & src) const;
 
  // Q criterion
  void
  compute_q_criterion(VectorType & dst, VectorType const & src) const;
 
  /*
   * Operators.
   */
 
  // mass operator
  void
  apply_mass_operator(VectorType & dst, VectorType const & src) const;
 
  void
  apply_mass_operator_add(VectorType & dst, VectorType const & src) const;
 
  // body force term
  void
  evaluate_add_body_force_term(VectorType & dst, double const time) const;
 
  // convective term
  void
  evaluate_convective_term(VectorType & dst, VectorType const & src, Number const time) const;
 
  // pressure gradient term
  void
  evaluate_pressure_gradient_term(VectorType &       dst,
                                  VectorType const & src,
                                  double const       time) const;
 
  // velocity divergence
  void
  evaluate_velocity_divergence_term(VectorType &       dst,
                                    VectorType const & src,
                                    double const       time) const;
 
  // inverse velocity mass operator
  unsigned int
  apply_inverse_mass_operator(VectorType & dst, VectorType const & src) const;
 
  /*
   * Update variable viscosity.
   */
  void
  update_viscosity(VectorType const & velocity) const;
 
  /*
   * Projection step.
   */
  void
  update_projection_operator(VectorType const & velocity, double const time_step_size) const;
 
  void
  rhs_add_projection_operator(VectorType & dst, double const time) const;
 
  unsigned int
  solve_projection(VectorType &       dst,
                   VectorType const & src,
                   bool const &       update_preconditioner) const;
 
  /*
   * Postprocessing.
   */
  double
  calculate_dissipation_convective_term(VectorType const & velocity, double const time) const;
 
  double
  calculate_dissipation_viscous_term(VectorType const & velocity) const;
 
  double
  calculate_dissipation_divergence_term(VectorType const & velocity) const;
 
  double
  calculate_dissipation_continuity_term(VectorType const & velocity) const;
 
  /*
   * Updates operators after grid has been moved.
   */
  virtual void
  update_after_grid_motion(bool const update_matrix_free);
 
  /*
   * Sets the grid velocity.
   */
  void
  set_grid_velocity(VectorType const & velocity);
 
  /*
   *  Calls constraint_u.distribute(u) and updates the constrained DoFs of the velocity field
   */
  void
  distribute_constraint_u(VectorType & velocity) const;
 
protected:
  /*
   * Projection step.
   */
  void
  setup_projection_solver();
 
  bool
  unsteady_problem_has_to_be_solved() const;
 
  /*
   * Grid
   */
  std::shared_ptr<Grid<dim> const> grid;
 
  /*
   * dealii::Mapping (In case of moving meshes (ALE), this is the dynamic mapping describing the
   * deformed configuration.)
   */
  std::shared_ptr<dealii::Mapping<dim> const> mapping;
 
  std::shared_ptr<MultigridMappings<dim, Number>> const multigrid_mappings;
 
  /*
   * User interface: Boundary conditions and field functions.
   */
  std::shared_ptr<BoundaryDescriptor<dim> const> boundary_descriptor;
  std::shared_ptr<FieldFunctions<dim> const>     field_functions;
 
  /*
   * List of parameters.
   */
  Parameters const & param;
 
  /*
   * A name describing the field being solved.
   */
  std::string const field;
 
  /*
   * In case of projection type incompressible Navier-Stokes solvers this variable is needed to
   * solve the pressure Poisson equation. However, this variable is also needed in case of a
   * coupled solution approach. In that case, it is used for the block preconditioner (or more
   * precisely for the Schur-complement preconditioner and the preconditioner used to approximately
   * invert the Laplace operator).
   *
   * While the functions specified in BoundaryDescriptorLaplace are relevant for projection-type
   * solvers (pressure Poisson equation has to be solved), the function specified in
   * BoundaryDescriptorLaplace are irrelevant for a coupled solution approach (since the pressure
   * Poisson operator is only needed for preconditioning, and hence, only the homogeneous part of
   * the operator has to be evaluated so that the boundary conditions are never applied).
   *
   */
  std::shared_ptr<Poisson::BoundaryDescriptor<0, dim>> boundary_descriptor_laplace;
 
  /*
   * Special case: pure Dirichlet boundary conditions.
   */
  dealii::Point<dim>              first_point;
  dealii::types::global_dof_index dof_index_first_point;
 
  /*
   * Element variable used to store the current physical time. This variable is needed for the
   * evaluation of certain integrals or weak forms.
   */
  mutable double evaluation_time;
 
private:
  /*
   * Basic finite element ingredients.
   */
  std::shared_ptr<dealii::FiniteElement<dim>> fe_u;
  std::shared_ptr<dealii::FiniteElement<dim>> fe_p;
  std::shared_ptr<dealii::FiniteElement<dim>> fe_u_scalar;
 
  dealii::DoFHandler<dim> dof_handler_u;
  dealii::DoFHandler<dim> dof_handler_p;
  dealii::DoFHandler<dim> dof_handler_u_scalar;
 
  dealii::AffineConstraints<Number> constraint_u, constraint_p, constraint_u_scalar;
 
  std::string const dof_index_u        = "velocity";
  std::string const dof_index_p        = "pressure";
  std::string const dof_index_u_scalar = "velocity_scalar";
 
  std::string const quad_index_u                 = "velocity";
  std::string const quad_index_p                 = "pressure";
  std::string const quad_index_u_overintegration = "velocity_overintegration";
  std::string const quad_index_u_nodal_points    = "velocity_nodal_points";
  std::string const quad_index_p_nodal_points    = "pressure_nodal_points";
 
  std::shared_ptr<MatrixFreeData<dim, Number> const>     matrix_free_data;
  std::shared_ptr<dealii::MatrixFree<dim, Number> const> matrix_free;
 
  // If we want to be able to update the mapping, we need a pointer to a non-const MatrixFree
  // object. In case this object is created, we let the above object called matrix_free point to
  // matrix_free_own_storage. This variable is needed for ALE formulations.
  std::shared_ptr<dealii::MatrixFree<dim, Number>> matrix_free_own_storage;
 
  bool pressure_level_is_undefined;
 
  /*
   * Interface coupling
   */
  std::shared_ptr<ContainerInterfaceData<1, dim, double>> interface_data_dirichlet_cached;
 
protected:
  /*
   * Operator kernels.
   */
  Operators::ConvectiveKernelData convective_kernel_data;
  Operators::ViscousKernelData    viscous_kernel_data;
 
  std::shared_ptr<Operators::ConvectiveKernel<dim, Number>> convective_kernel;
  std::shared_ptr<Operators::ViscousKernel<dim, Number>>    viscous_kernel;
 
  std::shared_ptr<Operators::DivergencePenaltyKernel<dim, Number>> div_penalty_kernel;
  std::shared_ptr<Operators::ContinuityPenaltyKernel<dim, Number>> conti_penalty_kernel;
 
  /*
   * Basic operators.
   */
  MassOperator<dim, dim, Number>  mass_operator;
  ConvectiveOperator<dim, Number> convective_operator;
  ViscousOperator<dim, Number>    viscous_operator;
  RHSOperator<dim, Number>        rhs_operator;
  GradientOperator<dim, Number>   gradient_operator;
  DivergenceOperator<dim, Number> divergence_operator;
 
  DivergencePenaltyOperator<dim, Number> div_penalty_operator;
  ContinuityPenaltyOperator<dim, Number> conti_penalty_operator;
 
  /*
   * Linear(ized) momentum operator.
   */
  mutable MomentumOperator<dim, Number> momentum_operator;
 
  /*
   * Inverse mass operator (for L2 spaces)
   */
  InverseMassOperator<dim, dim, Number> inverse_mass_velocity;
  InverseMassOperator<dim, 1, Number>   inverse_mass_velocity_scalar;
 
  /*
   * Inverse mass operator used in case of H(div)-conforming space
   */
  InverseMassOperatorHdiv<dim, dim, Number> inverse_mass_hdiv;
 
  /*
   * Projection operator.
   */
  typedef ProjectionOperator<dim, Number> ProjOperator;
  std::shared_ptr<ProjOperator>           projection_operator;
 
  /*
   * Projection solver.
   */
 
  // Elementwise solver/preconditioner used in case that only the divergence penalty term is used
  // and the system of equations is block-diagonal.
  typedef Elementwise::OperatorBase<dim, Number, ProjOperator> ELEMENTWISE_PROJ_OPERATOR;
  std::shared_ptr<ELEMENTWISE_PROJ_OPERATOR>                   elementwise_projection_operator;
 
  typedef Elementwise::PreconditionerBase<dealii::VectorizedArray<Number>>
                                              ELEMENTWISE_PRECONDITIONER;
  std::shared_ptr<ELEMENTWISE_PRECONDITIONER> elementwise_preconditioner_projection;
 
  // global solver/preconditioner to be used if the continuity penalty term is applied.
  std::shared_ptr<Krylov::SolverBase<VectorType>> projection_solver;
  std::shared_ptr<PreconditionerBase<Number>>     preconditioner_projection;
 
  /*
   * Calculators used to obtain derived quantities.
   */
  VorticityCalculator<dim, Number>  vorticity_calculator;
  DivergenceCalculator<dim, Number> divergence_calculator;
  ShearRateCalculator<dim, Number>  shear_rate_calculator;
  MagnitudeCalculator<dim, Number>  magnitude_calculator;
  QCriterionCalculator<dim, Number> q_criterion_calculator;
 
  MPI_Comm const mpi_comm;
 
  dealii::ConditionalOStream pcout;
 
private:
  // Minimum element length h_min required for global CFL condition.
  double
  calculate_minimum_element_length() const;
 
  /*
   * Initialization functions called during setup phase.
   */
  void
  initialize_boundary_descriptor_laplace();
 
  void
  initialize_dof_handler_and_constraints();
 
  void
  initialize_dirichlet_cached_bc();
 
  void
  initialize_operators(std::string const & dof_index_temperature);
 
  void
  initialize_calculators_for_derived_quantities();
 
  void
  initialization_pure_dirichlet_bc();
 
  void
  cell_loop_empty(dealii::MatrixFree<dim, Number> const &,
                  VectorType &,
                  VectorType const &,
                  Range const &) const
  {
  }
 
  void
  face_loop_empty(dealii::MatrixFree<dim, Number> const &,
                  VectorType &,
                  VectorType const &,
                  Range const &) const
  {
  }
 
  void
  local_interpolate_stress_bc_boundary_face(dealii::MatrixFree<dim, Number> const & matrix_free,
                                            VectorType &                            dst,
                                            VectorType const &                      src,
                                            Range const & face_range) const;
 
  // Interpolation of stress requires velocity and pressure, but the MatrixFree interface
  // only provides one argument, so we store pointers to have access to both velocity and
  // pressure.
  mutable VectorType const * velocity_ptr;
  mutable VectorType const * pressure_ptr;
 
  /*
   * Variable viscosity models.
   */
  mutable TurbulenceModel<dim, Number>           turbulence_model;
  mutable GeneralizedNewtonianModel<dim, Number> generalized_newtonian_model;
};
 
} // namespace IncNS
} // namespace ExaDG
 
#endif /* INCLUDE_EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_SPATIAL_OPERATOR_BASE_H_ \
        */