stokes.cc

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/*===========================================================================
 
 Copyright (C) 2002-2020 Yves Renard, Julien Pommier.
 
 This file is a part of GetFEM
 
 GetFEM  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 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 Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
 
===========================================================================*/
 
/**
   @file stokes.cc
   @brief Solve the stokes problem (incompressible viscuous fluid).
   
   This program is used to check that getfem++ is working. This is also 
   a good example of use of GetFEM.
   
   This file is almost identical to @link elastostatic.cc
   tests/elastostatic.cc@endlink, except than a
   linear incompressibility brick is inserted.
*/
 
#include "getfem/getfem_assembling.h" /* import assembly methods (and norms comp.) */
#include "getfem/getfem_export.h"   /* export functions (save solution in a file)  */
#include "getfem/getfem_regular_meshes.h"
#include "getfem/getfem_model_solvers.h"
#include "gmm/gmm.h"
using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;
 
/* some GetFEM types that we will be using */
using bgeot::base_small_vector; /* special class for small (dim<16) vectors */
using bgeot::base_node;  /* geometrical nodes(derived from base_small_vector)*/
using bgeot::scalar_type; /* = double */
using bgeot::size_type;   /* = unsigned long */
using bgeot::base_matrix; /* small dense matrix. */
 
/* definition of some matrix/vector types. These ones are built
 * using the predefined types in Gmm++
 */
typedef getfem::modeling_standard_sparse_vector sparse_vector;
typedef getfem::modeling_standard_sparse_matrix sparse_matrix;
typedef getfem::modeling_standard_plain_vector  plain_vector;
 
/*
 * structure for the stokes problem
 */
struct stokes_problem {
 
  enum { DIRICHLET_BOUNDARY_NUM = 0, NEUMANN_BOUNDARY_NUM = 1};
  getfem::mesh mesh;         /* the mesh */
  getfem::mesh_im  mim;      /* integration methods.                         */
  getfem::mesh_fem mf_u;     /* main mesh_fem, for the velocity              */
  getfem::mesh_fem mf_p;     /* mesh_fem for the pressure                    */
  getfem::mesh_fem mf_rhs;   /* mesh_fem for the right hand side (f(x),..)   */
  scalar_type nu;            /* Lam� coefficients.                           */
 
  scalar_type residual;        /* max residual for the iterative solvers         */
 
  std::string datafilename;
  bgeot::md_param PARAM;
 
  bool solve(plain_vector &U);
  void init(void);
  stokes_problem(void) : mim(mesh), mf_u(mesh), mf_p(mesh),
                         mf_rhs(mesh) {}
};
 
/* Read parameters from the .param file, build the mesh, set finite element
 * and integration methods and selects the boundaries.
 */
void stokes_problem::init(void) {
  std::string MESH_TYPE = PARAM.string_value("MESH_TYPE","Mesh type ");
  std::string FEM_TYPE  = PARAM.string_value("FEM_TYPE","FEM name");
  std::string FEM_TYPE_P  = PARAM.string_value("FEM_TYPE_P","FEM name P");
  std::string INTEGRATION = PARAM.string_value("INTEGRATION",
                                               "Name of integration method");
  cout << "MESH_TYPE=" << MESH_TYPE << "\n";
  cout << "FEM_TYPE="  << FEM_TYPE << "\n";
  cout << "INTEGRATION=" << INTEGRATION << "\n";
 
  /* First step : build the mesh */
  bgeot::pgeometric_trans pgt = 
    bgeot::geometric_trans_descriptor(MESH_TYPE);
  size_type N = pgt->dim();
  std::vector<size_type> nsubdiv(N);
  std::fill(nsubdiv.begin(),nsubdiv.end(),
            PARAM.int_value("NX", "Nomber of space steps "));
  getfem::regular_unit_mesh(mesh, nsubdiv, pgt,
                            PARAM.int_value("MESH_NOISED") != 0);
  
  /* scale the unit mesh to [LX,LY,..] and incline it */
   bgeot::base_matrix M(N,N);
  for (size_type i=0; i < N; ++i) {
    static const char *t[] = {"LX","LY","LZ"};
    M(i,i) = (i<3) ? PARAM.real_value(t[i],t[i]) : 1.0;
  }
  mesh.transformation(M);
 
  datafilename = PARAM.string_value("ROOTFILENAME","Base name of data files.");
  residual = PARAM.real_value("RESIDUAL"); if (residual == 0.) residual = 1e-10;
 
  nu = PARAM.real_value("NU", "Viscosit�);
  mf_u.set_qdim(bgeot::dim_type(N));

  /* set the finite element on the mf_u */
  getfem::pfem pf_u = 
    getfem::fem_descriptor(FEM_TYPE);
  getfem::pintegration_method ppi = 
    getfem::int_method_descriptor(INTEGRATION); 

  mim.set_integration_method(mesh.convex_index(), ppi);
  mf_u.set_finite_element(mesh.convex_index(), pf_u);
  mf_p.set_finite_element(mesh.convex_index(),
                          getfem::fem_descriptor(FEM_TYPE_P));

  /* set the finite element on mf_rhs (same as mf_u is DATA_FEM_TYPE is
     not used in the .param file */
  std::string data_fem_name = PARAM.string_value("DATA_FEM_TYPE");
  if (data_fem_name.size() == 0) {
    GMM_ASSERT1(pf_u->is_lagrange(), "You are using a non-lagrange FEM "
                << data_fem_name << ". In that case you need to set "
                << "DATA_FEM_TYPE in the .param file");
    mf_rhs.set_finite_element(mesh.convex_index(), pf_u);
  } else {
    mf_rhs.set_finite_element(mesh.convex_index(), 
                              getfem::fem_descriptor(data_fem_name));
  }
  
  /* set boundary conditions
   * (Neuman on the upper face, Dirichlet elsewhere) */
  cout << "Selecting Neumann and Dirichlet boundaries\n";
  getfem::mesh_region border_faces;
  getfem::outer_faces_of_mesh(mesh, border_faces);
  for (getfem::mr_visitor it(border_faces); !it.finished(); ++it) {
    assert(it.is_face());
    base_node un = mesh.normal_of_face_of_convex(it.cv(), it.f());
    un /= gmm::vect_norm2(un);
    if (gmm::abs(un[N-1] - 1.0) < 1.0E-7) { // new Neumann face
      mesh.region(NEUMANN_BOUNDARY_NUM).add(it.cv(), it.f());
    } else {
      mesh.region(DIRICHLET_BOUNDARY_NUM).add(it.cv(), it.f());
    }
  }
}

/**************************************************************************/
/*  Model.                                                                */
/**************************************************************************/

base_small_vector sol_f(const base_small_vector &P) {
  base_small_vector res(P.size());
  res[P.size()-1] = -1.0;
  return res;
}


bool stokes_problem::solve(plain_vector &U) {
  size_type N = mesh.dim();

  getfem::model model;

  // Main unknown of the problem.
  model.add_fem_variable("u", mf_u);

  // Linearized elasticity brick.
  model.add_initialized_fixed_size_data
    ("lambda", plain_vector(1, 0.0));
  model.add_initialized_fixed_size_data("nu", plain_vector(1, nu));
  getfem::add_isotropic_linearized_elasticity_brick
    (model, mim, "u", "lambda", "nu");

  // Linearized incompressibility condition brick.
  model.add_fem_variable("p", mf_p); // Adding the pressure as a variable
  add_linear_incompressibility(model, mim, "u", "p");

  // Volumic source term.
  std::vector<scalar_type> F(mf_rhs.nb_dof()*N);
  getfem::interpolation_function(mf_rhs, F, sol_f);
  model.add_initialized_fem_data("VolumicData", mf_rhs, F);
  getfem::add_source_term_brick(model, mim, "u", "VolumicData");

  // Dirichlet condition.
  gmm::clear(F);
  model.add_initialized_fem_data("DirichletData", mf_rhs, F);
  getfem::add_Dirichlet_condition_with_multipliers
    (model, mim, "u", mf_u, DIRICHLET_BOUNDARY_NUM, "DirichletData");

  gmm::iteration iter(residual, 1, 40000);
  getfem::standard_solve(model, iter);

  // Solution extraction
  gmm::copy(model.real_variable("u"), U);
  
  return (iter.converged());
}

/**************************************************************************/
/*  main program.                                                         */
/**************************************************************************/

int main(int argc, char *argv[]) {

  GETFEM_MPI_INIT(argc, argv);
  GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
  FE_ENABLE_EXCEPT;        // Enable floating point exception for Nan.

  try {    
    stokes_problem p;
    p.PARAM.read_command_line(argc, argv);
    p.init();
    // p.mesh.write_to_file(p.datafilename + ".mesh");
    plain_vector U(p.mf_u.nb_dof());
    if (!p.solve(U)) GMM_ASSERT1(false, "Solve has failed");
    if (p.PARAM.int_value("VTK_EXPORT")) {
      cout << "export to " << p.datafilename + ".vtk" << "..\n";
      getfem::vtk_export exp(p.datafilename + ".vtk",
                             p.PARAM.int_value("VTK_EXPORT")==1);
      exp.exporting(p.mf_u); 
      exp.write_point_data(p.mf_u, U, "stokes_displacement");
      cout << "export done, you can view the data file with (for example)\n"
        "mayavi2 -d " << p.datafilename << ".vtk -f ExtractVectorNorm -f "
        "WarpVector -m Surface -m Outline\n";
    }
  }
  GMM_STANDARD_CATCH_ERROR;
  GETFEM_MPI_FINALIZE;

  return 0; 
}
");
  mf_u.set_qdim(bgeot::dim_type(N));
 
  /* set the finite element on the mf_u */
  getfem::pfem pf_u = 
    getfem::fem_descriptor(FEM_TYPE);
  getfem::pintegration_method ppi = 
    getfem::int_method_descriptor(INTEGRATION); 
 
  mim.set_integration_method(mesh.convex_index(), ppi);
  mf_u.set_finite_element(mesh.convex_index(), pf_u);
  mf_p.set_finite_element(mesh.convex_index(),
                          getfem::fem_descriptor(FEM_TYPE_P));
 
  /* set the finite element on mf_rhs (same as mf_u is DATA_FEM_TYPE is
     not used in the .param file */
  std::string data_fem_name = PARAM.string_value("DATA_FEM_TYPE");
  if (data_fem_name.size() == 0) {
    GMM_ASSERT1(pf_u->is_lagrange(), "You are using a non-lagrange FEM "
                << data_fem_name << ". In that case you need to set "
                << "DATA_FEM_TYPE in the .param file");
    mf_rhs.set_finite_element(mesh.convex_index(), pf_u);
  } else {
    mf_rhs.set_finite_element(mesh.convex_index(), 
                              getfem::fem_descriptor(data_fem_name));
  }
  
  /* set boundary conditions
   * (Neuman on the upper face, Dirichlet elsewhere) */
  cout << "Selecting Neumann and Dirichlet boundaries\n";
  getfem::mesh_region border_faces;
  getfem::outer_faces_of_mesh(mesh, border_faces);
  for (getfem::mr_visitor it(border_faces); !it.finished(); ++it) {
    assert(it.is_face());
    base_node un = mesh.normal_of_face_of_convex(it.cv(), it.f());
    un /= gmm::vect_norm2(un);
    if (gmm::abs(un[N-1] - 1.0) < 1.0E-7) { // new Neumann face
      mesh.region(NEUMANN_BOUNDARY_NUM).add(it.cv(), it.f());
    } else {
      mesh.region(DIRICHLET_BOUNDARY_NUM).add(it.cv(), it.f());
    }
  }
}
 
/**************************************************************************/
/*  Model.                                                                */
/**************************************************************************/
 
base_small_vector sol_f(const base_small_vector &P) {
  base_small_vector res(P.size());
  res[P.size()-1] = -1.0;
  return res;
}
 
 
bool stokes_problem::solve(plain_vector &U) {
  size_type N = mesh.dim();
 
  getfem::model model;
 
  // Main unknown of the problem.
  model.add_fem_variable("u", mf_u);
 
  // Linearized elasticity brick.
  model.add_initialized_fixed_size_data
    ("lambda", plain_vector(1, 0.0));
  model.add_initialized_fixed_size_data("nu", plain_vector(1, nu));
  getfem::add_isotropic_linearized_elasticity_brick
    (model, mim, "u", "lambda", "nu");
 
  // Linearized incompressibility condition brick.
  model.add_fem_variable("p", mf_p); // Adding the pressure as a variable
  add_linear_incompressibility(model, mim, "u", "p");
 
  // Volumic source term.
  std::vector<scalar_type> F(mf_rhs.nb_dof()*N);
  getfem::interpolation_function(mf_rhs, F, sol_f);
  model.add_initialized_fem_data("VolumicData", mf_rhs, F);
  getfem::add_source_term_brick(model, mim, "u", "VolumicData");
 
  // Dirichlet condition.
  gmm::clear(F);
  model.add_initialized_fem_data("DirichletData", mf_rhs, F);
  getfem::add_Dirichlet_condition_with_multipliers
    (model, mim, "u", mf_u, DIRICHLET_BOUNDARY_NUM, "DirichletData");
 
  gmm::iteration iter(residual, 1, 40000);
  getfem::standard_solve(model, iter);
 
  // Solution extraction
  gmm::copy(model.real_variable("u"), U);
  
  return (iter.converged());
}
 
/**************************************************************************/
/*  main program.                                                         */
/**************************************************************************/
 
int main(int argc, char *argv[]) {
 
  GETFEM_MPI_INIT(argc, argv);
  GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
  FE_ENABLE_EXCEPT;        // Enable floating point exception for Nan.
 
  try {    
    stokes_problem p;
    p.PARAM.read_command_line(argc, argv);
    p.init();
    // p.mesh.write_to_file(p.datafilename + ".mesh");
    plain_vector U(p.mf_u.nb_dof());
    if (!p.solve(U)) GMM_ASSERT1(false, "Solve has failed");
    if (p.PARAM.int_value("VTK_EXPORT")) {
      cout << "export to " << p.datafilename + ".vtk" << "..\n";
      getfem::vtk_export exp(p.datafilename + ".vtk",
                             p.PARAM.int_value("VTK_EXPORT")==1);
      exp.exporting(p.mf_u); 
      exp.write_point_data(p.mf_u, U, "stokes_displacement");
      cout << "export done, you can view the data file with (for example)\n"
        "mayavi2 -d " << p.datafilename << ".vtk -f ExtractVectorNorm -f "
        "WarpVector -m Surface -m Outline\n";
    }
  }
  GMM_STANDARD_CATCH_ERROR;
  GETFEM_MPI_FINALIZE;
 
  return 0; 
}