int main(int argc, char *argv[])
{
MeshView v;
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
// create the application window
v.create(argc, argv);
// run the application
glutMainLoop();
return 0;
}
int main(int argc, char* argv[])
{
if (argc != 2)
{
printf("Usage: meshview mesh-filename\n");
exit(1);
}
Mesh mesh;
mesh.load(argv[1], true);
MeshView mv;
mv.show(&mesh);
View::wait();
return 0;
}
int main(int argc, char* args[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("square.mesh", &mesh);
// Perform initial mesh refinement.
for (int i=0; i<INIT_REF; i++)
mesh.refine_all_elements();
mesh.refine_by_criterion(criterion, INIT_REF_CRITERION);
MeshView m;
m.show(&mesh);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver_type);
Vector<double>* rhs = create_vector<double>(matrix_solver_type);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver_type, matrix, rhs);
ScalarView view1("Solution - Discontinuous Galerkin FEM", new WinGeom(900, 0, 450, 350));
ScalarView view2("Solution - Standard continuous FEM", new WinGeom(900, 400, 450, 350));
if(WANT_DG)
{
// Create an L2 space.
L2Space<double> space_l2(&mesh, P_INIT);
// Initialize the solution.
Solution<double> sln_l2;
// Initialize the weak formulation.
CustomWeakForm wf_l2(BDY_BOTTOM_LEFT);
// Initialize the FE problem.
DiscreteProblem<double> dp_l2(&wf_l2, &space_l2);
info("Assembling Discontinuous Galerkin (nelem: %d, ndof: %d).", mesh.get_num_active_elements(), space_l2.get_num_dofs());
dp_l2.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving Discontinuous Galerkin.");
if(solver->solve())
if(DG_SHOCK_CAPTURING)
{
FluxLimiter flux_limiter(FluxLimiter::Kuzmin, solver->get_sln_vector(), &space_l2, true);
flux_limiter.limit_second_orders_according_to_detector();
flux_limiter.limit_according_to_detector();
flux_limiter.get_limited_solution(&sln_l2);
view1.set_title("Solution - limited Discontinuous Galerkin FEM");
}
else
Solution<double>::vector_to_solution(solver->get_sln_vector(), &space_l2, &sln_l2);
else
error ("Matrix solver failed.\n");
// View the solution.
view1.show(&sln_l2);
}
if(WANT_FEM)
{
// Create an H1 space.
H1Space<double> space_h1(&mesh, P_INIT);
// Initialize the solution.
Solution<double> sln_h1;
// Initialize the weak formulation.
CustomWeakForm wf_h1(BDY_BOTTOM_LEFT, false);
// Initialize the FE problem.
DiscreteProblem<double> dp_h1(&wf_h1, &space_h1);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver_type);
Vector<double>* rhs = create_vector<double>(matrix_solver_type);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver_type, matrix, rhs);
info("Assembling Continuous FEM (nelem: %d, ndof: %d).", mesh.get_num_active_elements(), space_h1.get_num_dofs());
dp_h1.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving Continuous FEM.");
if(solver->solve())
Solution<double>::vector_to_solution(solver->get_sln_vector(), &space_h1, &sln_h1);
else
error ("Matrix solver failed.\n");
// View the solution.
view2.show(&sln_h1);
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
// Wait for keyboard or mouse input.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2DXML mloader;
mloader.load("domain-arcs.xml", &mesh);
mesh.refine_towards_boundary(BDY_SOLID_WALL_PROFILE, INIT_REF_NUM_BOUNDARY_ANISO, true, true);
mesh.refine_towards_vertex(0, INIT_REF_NUM_VERTEX, true);
MeshView m;
m.show(&mesh);
m.wait_for_close();
// Initialize boundary condition types and spaces with default shapesets.
L2Space<double>space_rho(&mesh, P_INIT);
L2Space<double>space_rho_v_x(&mesh, P_INIT);
L2Space<double>space_rho_v_y(&mesh, P_INIT);
L2Space<double>space_e(&mesh, P_INIT);
int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double>*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
info("Initial coarse ndof: %d", ndof);
// Initialize solutions, set initial conditions.
ConstantSolution<double> sln_rho(&mesh, RHO_EXT);
ConstantSolution<double> sln_rho_v_x(&mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> sln_rho_v_y(&mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> sln_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
ConstantSolution<double> prev_rho(&mesh, RHO_EXT);
ConstantSolution<double> prev_rho_v_x(&mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> prev_rho_v_y(&mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> prev_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
Solution<double> rsln_rho, rsln_rho_v_x, rsln_rho_v_y, rsln_e;
// Numerical flux.
VijayasundaramNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
EulerEquationsWeakFormSemiImplicitMultiComponent wf(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL, BDY_SOLID_WALL_PROFILE,
BDY_INLET, BDY_OUTLET, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e);
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA, RHO_EXT, P_EXT);
ScalarView pressure_view("Pressure", new WinGeom(0, 0, 600, 300));
ScalarView Mach_number_view("Mach number", new WinGeom(700, 0, 600, 300));
ScalarView entropy_production_view("Entropy estimate", new WinGeom(0, 400, 600, 300));
OrderView space_view("Space", new WinGeom(700, 400, 600, 300));
// Initialize refinement selector.
L2ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, MAX_P_ORDER);
selector.set_error_weights(1.0, 1.0, 1.0);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Look for a saved solution on the disk.
Continuity<double> continuity(Continuity<double>::onlyTime);
int iteration = 0; double t = 0;
bool loaded_now = false;
if(REUSE_SOLUTION && continuity.have_record_available())
{
continuity.get_last_record()->load_mesh(&mesh);
continuity.get_last_record()->load_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<SpaceType>(HERMES_L2_SPACE, HERMES_L2_SPACE, HERMES_L2_SPACE, HERMES_L2_SPACE), Hermes::vector<Mesh *>(&mesh, &mesh,
&mesh, &mesh));
continuity.get_last_record()->load_time_step_length(time_step);
t = continuity.get_last_record()->get_time() + time_step;
iteration = continuity.get_num() * EVERY_NTH_STEP + 1;
loaded_now = true;
}
// Time stepping loop.
for(; t < 5.0; t += time_step)
{
CFL.set_number(CFL_NUMBER + (t/5.0) * 10.0);
info("---- Time step %d, time %3.5f.", iteration++, t);
// Periodic global derefinements.
if (iteration > 1 && iteration % UNREF_FREQ == 0 && REFINEMENT_COUNT > 0)
{
info("Global mesh derefinement.");
REFINEMENT_COUNT = 0;
space_rho.unrefine_all_mesh_elements(true);
space_rho.adjust_element_order(-1, P_INIT);
space_rho_v_x.copy_orders(&space_rho);
space_rho_v_y.copy_orders(&space_rho);
space_e.copy_orders(&space_rho);
}
// Adaptivity loop:
int as = 1;
int ndofs_prev = 0;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
int order_increase = 1;
Hermes::vector<Space<double> *>* ref_spaces = Space<double>::construct_refined_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), order_increase);
Hermes::vector<const Space<double> *> ref_spaces_const((*ref_spaces)[0], (*ref_spaces)[1],
(*ref_spaces)[2], (*ref_spaces)[3]);
if(ndofs_prev != 0)
if(Space<double>::get_num_dofs(ref_spaces_const) == ndofs_prev)
selector.set_error_weights(2.0 * selector.get_error_weight_h(), 1.0, 1.0);
else
selector.set_error_weights(1.0, 1.0, 1.0);
ndofs_prev = Space<double>::get_num_dofs(ref_spaces_const);
// Project the previous time level solution onto the new fine mesh.
info("Projecting the previous time level solution onto the new fine mesh.");
if(loaded_now)
{
loaded_now = false;
continuity.get_last_record()->load_solutions(Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::vector<Space<double> *>((*ref_spaces)[0], (*ref_spaces)[1], (*ref_spaces)[2], (*ref_spaces)[3]));
}
else
{
OGProjection<double>::project_global(ref_spaces_const, Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), matrix_solver, Hermes::vector<Hermes::Hermes2D::ProjNormType>());
if(iteration > std::max((int)(continuity.get_num() * EVERY_NTH_STEP + 2), 1) && as > 1)
{
delete rsln_rho.get_mesh();
delete rsln_rho.get_space();
rsln_rho.own_mesh = false;
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_x.get_space();
rsln_rho_v_x.own_mesh = false;
delete rsln_rho_v_y.get_mesh();
delete rsln_rho_v_y.get_space();
rsln_rho_v_y.own_mesh = false;
delete rsln_e.get_mesh();
delete rsln_e.get_space();
rsln_e.own_mesh = false;
}
}
// Report NDOFs.
info("ndof_coarse: %d, ndof_fine: %d.",
Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e)), Space<double>::get_num_dofs(ref_spaces_const));
// Assemble the reference problem.
info("Solving on reference mesh.");
DiscreteProblem<double> dp(&wf, ref_spaces_const);
SparseMatrix<double>* matrix = create_matrix<double>(matrix_solver);
Vector<double>* rhs = create_vector<double>(matrix_solver);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver, matrix, rhs);
wf.set_time_step(time_step);
// Assemble the stiffness matrix and rhs.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the matrix problem.
info("Solving the matrix problem.");
if(solver->solve())
if(!SHOCK_CAPTURING)
Solution<double>::vector_to_solutions(solver->get_sln_vector(), ref_spaces_const,
Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
else
{
FluxLimiter flux_limiter(FluxLimiter::Kuzmin, solver->get_sln_vector(), ref_spaces_const, true);
flux_limiter.limit_second_orders_according_to_detector(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
flux_limiter.limit_according_to_detector(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
flux_limiter.get_limited_solutions(Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e));
}
else
error ("Matrix solver failed.\n");
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection<double>::project_global(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e),
Hermes::vector<Solution<double>*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), matrix_solver,
Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM));
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt<double>* adaptivity = new Adapt<double>(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM));
double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution<double>*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e),
Hermes::vector<Solution<double>*>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e)) * 100;
CFL.calculate_semi_implicit(Hermes::vector<Solution<double> *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), (*ref_spaces)[0]->get_mesh(), time_step);
// Report results.
info("err_est_rel: %g%%", err_est_rel_total);
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP)
done = true;
else
{
info("Adapting coarse mesh.");
if (Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e)) >= NDOF_STOP)
done = true;
else
{
REFINEMENT_COUNT++;
done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector<double> *>(&selector, &selector, &selector, &selector),
THRESHOLD, STRATEGY, MESH_REGULARITY);
}
if(!done)
as++;
}
// Visualization and saving on disk.
if(done && (iteration - 1) % EVERY_NTH_STEP == 0 && iteration > 1)
{
// Hermes visualization.
if(HERMES_VISUALIZATION)
{
Mach_number.reinit();
pressure.reinit();
entropy.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy);
Mach_number_view.show(&Mach_number);
pressure_view.save_numbered_screenshot("Pressure-%u.bmp", iteration - 1, true);
Mach_number_view.save_numbered_screenshot("Mach-%u.bmp", iteration - 1, true);
}
// Output solution in VTK format.
if(VTK_VISUALIZATION)
{
pressure.reinit();
Mach_number.reinit();
Linearizer lin;
char filename[40];
sprintf(filename, "Pressure-%i.vtk", iteration - 1);
lin.save_solution_vtk(&pressure, filename, "Pressure", false);
sprintf(filename, "Mach number-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", false);
}
// Save a current state on the disk.
if(iteration > 1)
{
continuity.add_record(t);
continuity.get_last_record()->save_mesh(&mesh);
continuity.get_last_record()->save_spaces(Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
continuity.get_last_record()->save_solutions(Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
continuity.get_last_record()->save_time_step_length(time_step);
}
}
// Clean up.
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
}
while (done == false);
// Copy the solutions into the previous time level ones.
prev_rho.copy(&rsln_rho);
prev_rho_v_x.copy(&rsln_rho_v_x);
prev_rho_v_y.copy(&rsln_rho_v_y);
prev_e.copy(&rsln_e);
delete rsln_rho.get_mesh();
delete rsln_rho.get_space();
rsln_rho.own_mesh = false;
delete rsln_rho_v_x.get_mesh();
delete rsln_rho_v_x.get_space();
rsln_rho_v_x.own_mesh = false;
delete rsln_rho_v_y.get_mesh();
delete rsln_rho_v_y.get_space();
rsln_rho_v_y.own_mesh = false;
delete rsln_e.get_mesh();
delete rsln_e.get_space();
rsln_e.own_mesh = false;
}
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
return 0;
}
void Scene::flip_selected_edge() {
MeshView *meshView = get_selection_as_mesh();
if (meshView == nullptr) return;
meshView->flip_selected_edge();
invalidate_selection();
}
void Scene::resample_selected_mesh() {
MeshView *meshView = get_selection_as_mesh();
if (meshView == nullptr) return;
meshView->resample();
invalidate_selection();
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("ffs.mesh", &mesh);
mesh.refine_by_criterion(refinement_criterion, INIT_REF_NUM_STEP);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++)
mesh.refine_all_elements(0, true);
MeshView m;
m.show(&mesh);
// Initialize boundary condition types and spaces with default shapesets.
L2Space<double> space_rho(&mesh, P_INIT);
L2Space<double> space_rho_v_x(&mesh, P_INIT);
L2Space<double> space_rho_v_y(&mesh, P_INIT);
L2Space<double> space_e(&mesh, P_INIT);
L2Space<double> space_stabilization(&mesh, 0);
int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double>*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
Hermes::Mixins::Loggable::Static::info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
ConstantSolution<double> prev_rho(&mesh, RHO_EXT);
ConstantSolution<double> prev_rho_v_x(&mesh, RHO_EXT * V1_EXT);
ConstantSolution<double> prev_rho_v_y(&mesh, RHO_EXT * V2_EXT);
ConstantSolution<double> prev_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA, RHO_EXT, P_EXT);
ScalarView pressure_view("Pressure", new WinGeom(0, 0, 600, 300));
ScalarView Mach_number_view("Mach number", new WinGeom(700, 0, 600, 300));
ScalarView entropy_production_view("Entropy estimate", new WinGeom(0, 400, 600, 300));
ScalarView s1("prev_rho", new WinGeom(0, 0, 600, 300));
ScalarView s2("prev_rho_v_x", new WinGeom(700, 0, 600, 300));
ScalarView s3("prev_rho_v_y", new WinGeom(0, 400, 600, 300));
ScalarView s4("prev_e", new WinGeom(700, 400, 600, 300));
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Look for a saved solution on the disk.
CalculationContinuity<double> continuity(CalculationContinuity<double>::onlyTime);
int iteration = 0; double t = 0;
if(REUSE_SOLUTION && continuity.have_record_available())
{
continuity.get_last_record()->load_mesh(&mesh);
Hermes::vector<Space<double> *> spaceVector = continuity.get_last_record()->load_spaces(Hermes::vector<Mesh *>(&mesh, &mesh, &mesh, &mesh));
space_rho.copy(spaceVector[0], &mesh);
space_rho_v_x.copy(spaceVector[1], &mesh);
space_rho_v_y.copy(spaceVector[2], &mesh);
space_e.copy(spaceVector[3], &mesh);
continuity.get_last_record()->load_solutions(Hermes::vector<Solution<double>*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), Hermes::vector<Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
continuity.get_last_record()->load_time_step_length(time_step);
t = continuity.get_last_record()->get_time();
iteration = continuity.get_num();
}
// Initialize weak formulation.
Hermes::vector<std::string> solid_wall_markers(BDY_SOLID_WALL_BOTTOM, BDY_SOLID_WALL_TOP);
Hermes::vector<std::string> inlet_markers;
inlet_markers.push_back(BDY_INLET);
Hermes::vector<std::string> outlet_markers;
outlet_markers.push_back(BDY_OUTLET);
EulerEquationsWeakFormSemiImplicit wf(KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT,solid_wall_markers,
inlet_markers, outlet_markers, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, (P_INIT == 0));
EulerEquationsWeakFormStabilization wf_stabilization(&prev_rho);
// Initialize the FE problem.
DiscreteProblemLinear<double> dp(&wf, Hermes::vector<const Space<double>*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
DiscreteProblem<double> dp_stabilization(&wf_stabilization, &space_stabilization);
LinearSolver<double> solver(&dp);
// If the FE problem is in fact a FV problem.
if(P_INIT == 0)
dp.set_fvm();
// Time stepping loop.
for(; t < 10.0; t += time_step)
{
Hermes::Mixins::Loggable::Static::info("---- Time step %d, time %3.5f.", iteration++, t);
CFL.set_number(0.1 + (t/7.0) * 1.0);
// Set the current time step.
wf.set_current_time_step(time_step);
// Assemble the stiffness matrix and rhs.
Hermes::Mixins::Loggable::Static::info("Assembling the stiffness matrix and right-hand side vector.");
// Solve the matrix problem.
Hermes::Mixins::Loggable::Static::info("Solving the matrix problem.");
try
{
solver.solve();
if(!SHOCK_CAPTURING)
{
Solution<double>::vector_to_solutions(solver.get_sln_vector(), Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution<double> *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
else
{
FluxLimiter* flux_limiter;
if(SHOCK_CAPTURING_TYPE == KUZMIN)
flux_limiter = new FluxLimiter(FluxLimiter::Kuzmin, solver.get_sln_vector(), Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), true);
else
flux_limiter = new FluxLimiter(FluxLimiter::Krivodonova, solver.get_sln_vector(), Hermes::vector<const Space<double> *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e));
if(SHOCK_CAPTURING_TYPE == KUZMIN)
flux_limiter->limit_second_orders_according_to_detector();
flux_limiter->limit_according_to_detector();
flux_limiter->get_limited_solutions(Hermes::vector<Solution<double> *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
}
catch(std::exception& e)
{
std::cout << e.what();
}
CFL.calculate(Hermes::vector<Solution<double> *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), &mesh, time_step);
// Visualization.
if((iteration - 1) % EVERY_NTH_STEP == 0)
{
// Hermes visualization.
if(HERMES_VISUALIZATION)
{
Mach_number.reinit();
pressure.reinit();
entropy.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy);
Mach_number_view.show(&Mach_number);
pressure_view.save_numbered_screenshot("Pressure-%u.bmp", iteration - 1, true);
Mach_number_view.save_numbered_screenshot("Mach-%u.bmp", iteration - 1, true);
}
// Output solution in VTK format.
if(VTK_VISUALIZATION)
{
pressure.reinit();
Mach_number.reinit();
Linearizer lin_pressure;
char filename[40];
sprintf(filename, "pressure-3D-%i.vtk", iteration - 1);
lin_pressure.save_solution_vtk(&pressure, filename, "Pressure", true);
Linearizer lin_mach;
sprintf(filename, "Mach number-3D-%i.vtk", iteration - 1);
lin_mach.save_solution_vtk(&Mach_number, filename, "MachNumber", true);
}
}
}
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Initial mesh refinements.
mesh->refine_all_elements();
mesh->refine_all_elements();
mesh->refine_towards_boundary(BDY_OBSTACLE, 2, false);
// 'true' stands for anisotropic refinements.
mesh->refine_towards_boundary(BDY_TOP, 2, true);
mesh->refine_towards_boundary(BDY_BOTTOM, 2, true);
// Show mesh.
MeshView mv;
mv.show(mesh);
Hermes::Mixins::Loggable::Static::info("Close mesh window to continue.");
// Initialize boundary conditions.
EssentialBCNonConst bc_left_vel_x(BDY_LEFT, VEL_INLET, H, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_other_vel_x({ BDY_BOTTOM, BDY_TOP, BDY_OBSTACLE }, 0.0);
EssentialBCs<double> bcs_vel_x({ &bc_left_vel_x, &bc_other_vel_x });
DefaultEssentialBCConst<double> bc_vel_y({ BDY_LEFT, BDY_BOTTOM, BDY_TOP, BDY_OBSTACLE }, 0.0);
EssentialBCs<double> bcs_vel_y(&bc_vel_y);
SpaceSharedPtr<double> xvel_space(new H1Space<double>(mesh, &bcs_vel_x, P_INIT_VEL));
SpaceSharedPtr<double> yvel_space(new H1Space<double>(mesh, &bcs_vel_y, P_INIT_VEL));
#ifdef PRESSURE_IN_L2
SpaceSharedPtr<double> p_space(new L2Space<double>(mesh, P_INIT_PRESSURE));
#else
SpaceSharedPtr<double> p_space(new H1Space<double>(mesh, P_INIT_PRESSURE));
#endif
std::vector<SpaceSharedPtr<double> > spaces({ xvel_space, yvel_space, p_space });
// Calculate and report the number of degrees of freedom.
int ndof = Space<double>::get_num_dofs(spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d.", ndof);
// Define projection norms.
NormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
NormType p_proj_norm = HERMES_L2_NORM;
#else
NormType p_proj_norm = HERMES_H1_NORM;
#endif
// Solutions for the Newton's iteration and time stepping.
Hermes::Mixins::Loggable::Static::info("Setting zero initial conditions.");
MeshFunctionSharedPtr<double> xvel_prev_time(new ZeroSolution<double>(mesh));
MeshFunctionSharedPtr<double> yvel_prev_time(new ZeroSolution<double>(mesh));
MeshFunctionSharedPtr<double> p_prev_time(new ZeroSolution<double>(mesh));
// Initialize weak formulation.
WeakFormSharedPtr<double> wf(new WeakFormNSNewton(STOKES, RE, TAU, xvel_prev_time, yvel_prev_time));
// Initialize the FE problem.
Hermes::Hermes2D::NewtonSolver<double> newton(wf, spaces);
Hermes::Mixins::Loggable::Static::info("Solving nonlinear problem:");
newton.set_max_allowed_iterations(NEWTON_MAX_ITER);
newton.set_tolerance(NEWTON_TOL, Hermes::Solvers::ResidualNormAbsolute);
newton.set_jacobian_constant();
// Initialize views.
VectorView vview("velocity [m/s]", new WinGeom(0, 0, 750, 240));
ScalarView pview("pressure [Pa]", new WinGeom(0, 290, 750, 240));
vview.set_min_max_range(0, 1.6);
vview.fix_scale_width(80);
//pview.set_min_max_range(-0.9, 1.0);
pview.fix_scale_width(80);
pview.show_mesh(true);
// Time-stepping loop:
char title[100];
int num_time_steps = T_FINAL / TAU;
for (int ts = 1; ts <= num_time_steps; ts++)
{
current_time += TAU;
Hermes::Mixins::Loggable::Static::info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
if (current_time <= STARTUP_TIME) {
Hermes::Mixins::Loggable::Static::info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(spaces, current_time);
}
// Perform Newton's iteration.
try
{
newton.solve();
}
catch (Hermes::Exceptions::Exception e)
{
e.print_msg();
};
// Update previous time level solutions.
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, { xvel_prev_time, yvel_prev_time, p_prev_time });
// Visualization.
// Hermes visualization.
if (HERMES_VISUALIZATION)
{
// Show the solution at the end of time step.
sprintf(title, "Velocity, time %g", current_time);
vview.set_title(title);
vview.show(xvel_prev_time, yvel_prev_time);
sprintf(title, "Pressure, time %g", current_time);
pview.set_title(title);
pview.show(p_prev_time);
}
}
// Wait for all views to be closed.
View::wait();
return 0;
}