int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("channel.mesh", &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(2);
//mesh.refine_towards_boundary(BDY_SOLID_WALL_BOTTOM, 2);
// Initialize boundary condition types and spaces with default shapesets.
L2Space space_rho(&mesh, P_INIT);
L2Space space_rho_v_x(&mesh, P_INIT);
L2Space space_rho_v_y(&mesh, P_INIT);
L2Space space_e(&mesh, P_INIT);
int ndof = Space::get_num_dofs(Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
InitialSolutionEulerDensity prev_rho(&mesh, RHO_EXT);
InitialSolutionEulerDensityVelX prev_rho_v_x(&mesh, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY prev_rho_v_y(&mesh, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy prev_e(&mesh, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
// Numerical flux.
StegerWarmingNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
EulerEquationsWeakFormExplicitMultiComponentSemiImplicit wf(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL_BOTTOM, BDY_SOLID_WALL_TOP,
BDY_INLET, BDY_OUTLET, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), is_linear);
// If the FE problem is in fact a FV problem.
//if(P_INIT == 0) dp.set_fvm();
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction*>(&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("1", new WinGeom(0, 0, 600, 300));
ScalarView s2("2", new WinGeom(700, 0, 600, 300));
ScalarView s3("3", new WinGeom(0, 400, 600, 300));
ScalarView s4("4", new WinGeom(700, 400, 600, 300));
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
int iteration = 0;
double t = 0;
for(t = 0.0; t < 3.0; t += time_step) {
info("---- Time step %d, time %3.5f.", iteration++, t);
// Set the current time step.
wf.set_time_step(time_step);
bool rhs_only = (iteration == 1 ? false : true);
// Assemble stiffness matrix and rhs or just rhs.
if (rhs_only == false) {
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
}
else {
info("Assembling the right-hand side vector (only).");
dp.assemble(NULL, rhs);
}
// Solve the matrix problem.
info("Solving the matrix problem.");
scalar* solution_vector = NULL;
if(solver->solve()) {
solution_vector = solver->get_solution();
Solution::vector_to_solutions(solution_vector, Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
else
error ("Matrix solver failed.\n");
if(SHOCK_CAPTURING) {
DiscontinuityDetector discontinuity_detector(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
std::set<int> discontinuous_elements = discontinuity_detector.get_discontinuous_element_ids(DISCONTINUITY_DETECTOR_PARAM);
FluxLimiter flux_limiter(solution_vector, Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
flux_limiter.limit_according_to_detector(discontinuous_elements);
}
if((iteration - 1) % CFL_CALC_FREQ == 0)
CFL.calculate(Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), &mesh, time_step);
// Visualization.
/*
Mach_number.reinit();
pressure.reinit();
entropy.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy);
Mach_number_view.show(&Mach_number);
*/
s1.show(&prev_rho);
s2.show(&prev_rho_v_x);
s3.show(&prev_rho_v_y);
s4.show(&prev_e);
View::wait();
}
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
s1.close();
s2.close();
s3.close();
s4.close();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("GAMM-channel.mesh", &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(1, 1);
mesh.refine_element(1053);
mesh.refine_element(1054);
mesh.refine_element(1087);
mesh.refine_element(1088);
mesh.refine_element(1117);
mesh.refine_element(1118);
mesh.refine_element(1151);
mesh.refine_element(1152);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_SOLID_WALL, BDY_INLET_OUTLET));
// Create L2 spaces with default shapesets.
L2Space space_rho(&mesh, &bc_types, P_INIT);
L2Space space_rho_v_x(&mesh, &bc_types, P_INIT);
L2Space space_rho_v_y(&mesh, &bc_types, P_INIT);
L2Space space_e(&mesh, &bc_types, P_INIT);
// Initialize solutions, set initial conditions.
Solution sln_rho, sln_rho_v_x, sln_rho_v_y, sln_e, prev_rho, prev_rho_v_x, prev_rho_v_y, prev_e;
sln_rho.set_exact(&mesh, ic_density);
sln_rho_v_x.set_exact(&mesh, ic_density_vel_x);
sln_rho_v_y.set_exact(&mesh, ic_density_vel_y);
sln_e.set_exact(&mesh, ic_energy);
prev_rho.set_exact(&mesh, ic_density);
prev_rho_v_x.set_exact(&mesh, ic_density_vel_x);
prev_rho_v_y.set_exact(&mesh, ic_density_vel_y);
prev_e.set_exact(&mesh, ic_energy);
// Initialize weak formulation.
WeakForm wf(4);
// Bilinear forms coming from time discretization by explicit Euler's method.
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0_time));
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1_time));
wf.add_matrix_form(2, 2, callback(bilinear_form_2_2_time));
wf.add_matrix_form(3, 3, callback(bilinear_form_3_3_time));
// Volumetric linear forms.
// Linear forms coming from the linearization by taking the Eulerian fluxes' Jacobian matrices
// from the previous time step.
// First flux.
// Unnecessary for FVM.
if(P_INIT.order_h > 0 || P_INIT.order_v > 0) {
wf.add_vector_form(0, callback(linear_form_0_1), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho_v_x));
wf.add_vector_form(1, callback(linear_form_1_0_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_first_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Second flux.
wf.add_vector_form(0, callback(linear_form_0_2), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_0_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_second_flux), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
// Volumetric linear forms coming from the time discretization.
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
wf.add_vector_form(0, linear_form_vector, linear_form_order, HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(1, linear_form_vector, linear_form_order, HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, linear_form_vector, linear_form_order, HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, linear_form_vector, linear_form_order, HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#else
wf.add_vector_form(0, linear_form, linear_form_order, HERMES_ANY, &prev_rho);
wf.add_vector_form(1, linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_x);
wf.add_vector_form(2, linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_y);
wf.add_vector_form(3, linear_form, linear_form_order, HERMES_ANY, &prev_e);
#endif
// Surface linear forms - inner edges coming from the DG formulation.
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
wf.add_vector_form_surf(0, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#else
wf.add_vector_form_surf(0, linear_form_interface_0, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, linear_form_interface_1, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, linear_form_interface_2, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, linear_form_interface_3, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#endif
// Surface linear forms - inlet / outlet edges.
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#else
wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_0, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_1, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_2, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_3, linear_form_order, BDY_INLET_OUTLET,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#endif
// Surface linear forms - Solid wall edges.
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#else
wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_0, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_1, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_2, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_3, linear_form_order, BDY_SOLID_WALL,
Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
#endif
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::Tuple<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), is_linear);
// If the FE problem is in fact a FV problem.
if(P_INIT.order_h == 0 && P_INIT.order_v == 0)
dp.set_fvm();
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
dp.use_vector_valued_forms();
#endif
// Filters for visualization of pressure and the two components of velocity.
SimpleFilter pressure(calc_pressure_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter u(calc_u_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter w(calc_w_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter Mach_number(calc_Mach_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter entropy_estimate(calc_entropy_estimate_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
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));
VectorView vview("Velocity", new WinGeom(700, 400, 600, 300));
// Iteration number.
int iteration = 0;
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Output of the approximate time derivative.
std::ofstream time_der_out("time_der");
for(t = 0.0; t < 10; t += TAU)
{
info("---- Time step %d, time %3.5f.", iteration, t);
iteration++;
bool rhs_only = (iteration == 1 ? false : true);
// Assemble stiffness matrix and rhs or just rhs.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
// Solve the matrix problem.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(), Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::Tuple<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
else
error ("Matrix solver failed.\n");
// Approximate the time derivative of the solution.
if(CALC_TIME_DER) {
Adapt *adapt_for_time_der_calc = new Adapt(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
bool solutions_for_adapt = false;
double difference = iteration == 1 ? 0 :
adapt_for_time_der_calc->calc_err_est(Hermes::Tuple<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::Tuple<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e),
(Hermes::Tuple<double>*) NULL, solutions_for_adapt,
HERMES_TOTAL_ERROR_ABS | HERMES_ELEMENT_ERROR_ABS) / TAU;
delete adapt_for_time_der_calc;
// Info about the approximate time derivative.
if(iteration > 1)
{
info("Approximate the norm time derivative : %g.", difference);
time_der_out << iteration << '\t' << difference << std::endl;
}
}
// Determine the time step according to the CFL condition.
// Only mean values on an element of each solution component are taken into account.
double *solution_vector = solver->get_solution();
double min_condition = 0;
Element *e;
for (int _id = 0, _max = mesh.get_max_element_id(); _id < _max; _id++) \
if (((e) = mesh.get_element_fast(_id))->used) \
if ((e)->active)
{
AsmList al;
space_rho.get_element_assembly_list(e, &al);
double rho = solution_vector[al.dof[0]];
space_rho_v_x.get_element_assembly_list(e, &al);
double v1 = solution_vector[al.dof[0]] / rho;
space_rho_v_y.get_element_assembly_list(e, &al);
double v2 = solution_vector[al.dof[0]] / rho;
space_e.get_element_assembly_list(e, &al);
double energy = solution_vector[al.dof[0]];
double condition = e->get_area() / (std::sqrt(v1*v1 + v2*v2) + calc_sound_speed(rho, rho*v1, rho*v2, energy));
if(condition < min_condition || min_condition == 0.)
min_condition = condition;
}
if(TAU > min_condition)
TAU = min_condition;
if(TAU < min_condition * 0.9)
TAU = min_condition;
// Copy the solutions into the previous time level ones.
prev_rho.copy(&sln_rho);
prev_rho_v_x.copy(&sln_rho_v_x);
prev_rho_v_y.copy(&sln_rho_v_y);
prev_e.copy(&sln_e);
// Visualization.
pressure.reinit();
u.reinit();
w.reinit();
Mach_number.reinit();
entropy_estimate.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy_estimate);
Mach_number_view.show(&Mach_number);
vview.show(&u, &w);
// If used, we need to clean the vector valued form caches.
#ifdef HERMES_USE_VECTOR_VALUED_FORMS
DiscreteProblem::empty_form_caches();
#endif
}
time_der_out.close();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh basemesh;
H2DReader mloader;
mloader.load("GAMM-channel.mesh", &basemesh);
// Initialize the meshes.
Mesh mesh_flow, mesh_concentration;
mesh_flow.copy(&basemesh);
mesh_concentration.copy(&basemesh);
for(unsigned int i = 0; i < INIT_REF_NUM_CONCENTRATION; i++)
mesh_concentration.refine_all_elements();
mesh_concentration.refine_towards_boundary(BDY_DIRICHLET_CONCENTRATION, INIT_REF_NUM_CONCENTRATION_BDY);
mesh_flow.refine_towards_boundary(BDY_DIRICHLET_CONCENTRATION, INIT_REF_NUM_CONCENTRATION_BDY);
for(unsigned int i = 0; i < INIT_REF_NUM_FLOW; i++)
mesh_flow.refine_all_elements();
// Initialize boundary condition types and spaces with default shapesets.
// For the concentration.
EssentialBCs bcs_concentration;
bcs_concentration.add_boundary_condition(new ConcentrationTimedepEssentialBC(BDY_DIRICHLET_CONCENTRATION, CONCENTRATION_EXT, CONCENTRATION_EXT_STARTUP_TIME));
bcs_concentration.add_boundary_condition(new ConcentrationTimedepEssentialBC(BDY_SOLID_WALL_TOP, 0.0, CONCENTRATION_EXT_STARTUP_TIME));
L2Space space_rho(&mesh_flow, P_INIT_FLOW);
L2Space space_rho_v_x(&mesh_flow, P_INIT_FLOW);
L2Space space_rho_v_y(&mesh_flow, P_INIT_FLOW);
L2Space space_e(&mesh_flow, P_INIT_FLOW);
// Space for concentration.
H1Space space_c(&mesh_concentration, &bcs_concentration, P_INIT_CONCENTRATION);
int ndof = Space::get_num_dofs(Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e, &space_c));
info("ndof: %d", ndof);
// Initialize solutions, set initial conditions.
InitialSolutionEulerDensity prev_rho(&mesh_flow, RHO_EXT);
InitialSolutionEulerDensityVelX prev_rho_v_x(&mesh_flow, RHO_EXT * V1_EXT);
InitialSolutionEulerDensityVelY prev_rho_v_y(&mesh_flow, RHO_EXT * V2_EXT);
InitialSolutionEulerDensityEnergy prev_e(&mesh_flow, QuantityCalculator::calc_energy(RHO_EXT, RHO_EXT * V1_EXT, RHO_EXT * V2_EXT, P_EXT, KAPPA));
InitialSolutionConcentration prev_c(&mesh_concentration, 0.0);
// Numerical flux.
OsherSolomonNumericalFlux num_flux(KAPPA);
// Initialize weak formulation.
EulerEquationsWeakFormSemiImplicitCoupled wf(&num_flux, KAPPA, RHO_EXT, V1_EXT, V2_EXT, P_EXT, BDY_SOLID_WALL_BOTTOM,
BDY_SOLID_WALL_TOP, BDY_INLET, BDY_OUTLET, BDY_NATURAL_CONCENTRATION, &prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c, EPSILON, (P_INIT_FLOW == 0));
wf.set_time_step(time_step);
// Initialize the FE problem.
DiscreteProblem dp(&wf, Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e, &space_c));
// If the FE problem is in fact a FV problem.
//if(P_INIT == 0) dp.set_fvm();
// Filters for visualization of Mach number, pressure and entropy.
MachNumberFilter Mach_number(Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
PressureFilter pressure(Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), KAPPA);
EntropyFilter entropy(Hermes::vector<MeshFunction*>(&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 s5("Concentration", new WinGeom(700, 400, 600, 300));
*/
ScalarView s1("1", new WinGeom(0, 0, 600, 300));
ScalarView s2("2", new WinGeom(700, 0, 600, 300));
ScalarView s3("3", new WinGeom(0, 400, 600, 300));
ScalarView s4("4", new WinGeom(700, 400, 600, 300));
ScalarView s5("Concentration", new WinGeom(350, 200, 600, 300));
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Set up CFL calculation class.
CFLCalculation CFL(CFL_NUMBER, KAPPA);
// Set up Advection-Diffusion-Equation stability calculation class.
ADEStabilityCalculation ADES(ADVECTION_STABILITY_CONSTANT, DIFFUSION_STABILITY_CONSTANT, EPSILON);
int iteration = 0; double t = 0;
for(t = 0.0; t < 100.0; t += time_step) {
info("---- Time step %d, time %3.5f.", iteration++, t);
// Set the current time step.
wf.set_time_step(time_step);
Space::update_essential_bc_values(&space_c, t);
// Assemble 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.");
scalar* solution_vector = NULL;
if(solver->solve()) {
solution_vector = solver->get_solution();
Solution::vector_to_solutions(solution_vector, Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e, &prev_c));
}
else
error ("Matrix solver failed.\n");
if(SHOCK_CAPTURING) {
DiscontinuityDetector discontinuity_detector(Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
std::set<int> discontinuous_elements = discontinuity_detector.get_discontinuous_element_ids(DISCONTINUITY_DETECTOR_PARAM);
FluxLimiter flux_limiter(solution_vector, Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
flux_limiter.limit_according_to_detector(discontinuous_elements);
}
util_time_step = time_step;
CFL.calculate_semi_implicit(Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), &mesh_flow, util_time_step);
time_step = util_time_step;
ADES.calculate(Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y), &mesh_concentration, util_time_step);
if(util_time_step < time_step)
time_step = util_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);
s5.show(&prev_c);
*/
s1.show(&prev_rho);
s2.show(&prev_rho_v_x);
s3.show(&prev_rho_v_y);
s4.show(&prev_e);
s5.show(&prev_c);
/*
s1.save_numbered_screenshot("density%i.bmp", iteration, true);
s2.save_numbered_screenshot("density_v_x%i.bmp", iteration, true);
s3.save_numbered_screenshot("density_v_y%i.bmp", iteration, true);
s4.save_numbered_screenshot("energy%i.bmp", iteration, true);
s5.save_numbered_screenshot("concentration%i.bmp", iteration, true);
*/
//s5.wait_for_close();
}
// 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, "pressure-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&pressure, filename, "Pressure", true);
sprintf(filename, "Mach number-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", false);
sprintf(filename, "Mach number-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&Mach_number, filename, "MachNumber", true);
sprintf(filename, "Concentration-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
sprintf(filename, "Concentration-3D-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "Concentration", true);
}
}
}
/*
pressure_view.close();
entropy_production_view.close();
Mach_number_view.close();
s5.close();
*/
s1.close();
s2.close();
s3.close();
s4.close();
s5.close();
return 0;
}
int main(int argc, char* argv[])
{
// Provide a possibility to change INITIAL_CONCENTRATION_STATE through an argument.
if(argc > 1)
INITIAL_CONCENTRATION_STATE = atoi(argv[1]);
if(argc > 2)
INIT_REF_NUM_FLOW = atoi(argv[2]);
if(argc > 3)
INIT_REF_NUM_CONCENTRATION = atoi(argv[3]);
// Load the mesh.
Mesh basemesh;
H2DReader mloader;
if(INITIAL_CONCENTRATION_STATE == 0)
mloader.load("GAMM-channel-4-bnds.mesh", &basemesh);
else
mloader.load("channel-4-bnds.mesh", &basemesh);
// Initialize the meshes.
Mesh mesh_flow, mesh_concentration;
mesh_flow.copy(&basemesh);
mesh_concentration.copy(&basemesh);
for(unsigned int i = 0; i < INIT_REF_NUM_CONCENTRATION; i++)
mesh_concentration.refine_all_elements();
for(unsigned int i = 0; i < INIT_REF_NUM_FLOW; i++)
mesh_flow.refine_all_elements();
// Initialize boundary condition types and spaces with default shapesets.
BCTypes bc_types_euler;
bc_types_euler.add_bc_neumann(Hermes::vector<int>(BDY_SOLID_WALL_TOP, BDY_SOLID_WALL_BOTTOM, BDY_INLET, BDY_OUTLET));
BCTypes bc_types_concentration;
BCValues bc_values_concentration;
switch(INITIAL_CONCENTRATION_STATE) {
case 0:
bc_types_concentration.add_bc_neumann(Hermes::vector<int>(BDY_INLET, BDY_OUTLET, BDY_SOLID_WALL_TOP));
bc_types_concentration.add_bc_dirichlet(Hermes::vector<int>(BDY_SOLID_WALL_BOTTOM));
bc_values_concentration.add_const(Hermes::vector<int>(BDY_SOLID_WALL_BOTTOM), CONCENTRATION_EXT);
break;
case 1:
bc_types_concentration.add_bc_neumann(Hermes::vector<int>(BDY_INLET, BDY_OUTLET, BDY_SOLID_WALL_TOP));
bc_types_concentration.add_bc_dirichlet(Hermes::vector<int>(BDY_SOLID_WALL_BOTTOM));
bc_values_concentration.add_const(Hermes::vector<int>(BDY_SOLID_WALL_BOTTOM), CONCENTRATION_EXT);
break;
case 2:
bc_types_concentration.add_bc_neumann(Hermes::vector<int>(BDY_SOLID_WALL_BOTTOM, BDY_OUTLET, BDY_SOLID_WALL_TOP));
bc_types_concentration.add_bc_dirichlet(Hermes::vector<int>(BDY_INLET));
bc_values_concentration.add_const(Hermes::vector<int>(BDY_INLET), CONCENTRATION_EXT);
break;
}
L2Space space_rho(&mesh_flow, &bc_types_euler, P_INIT_FLOW);
L2Space space_rho_v_x(&mesh_flow, &bc_types_euler, P_INIT_FLOW);
L2Space space_rho_v_y(&mesh_flow, &bc_types_euler, P_INIT_FLOW);
L2Space space_e(&mesh_flow, &bc_types_euler, P_INIT_FLOW);
// Space for concentration.
H1Space space_c(&mesh_concentration, &bc_types_concentration, &bc_values_concentration, P_INIT_CONCENTRATION);
// Initialize solutions, set initial conditions.
Solution sln_rho, sln_rho_v_x, sln_rho_v_y, sln_e, sln_c, prev_rho, prev_rho_v_x, prev_rho_v_y, prev_e, prev_c;
sln_rho.set_exact(&mesh_flow, ic_density);
sln_rho_v_x.set_exact(&mesh_flow, ic_density_vel_x);
sln_rho_v_y.set_exact(&mesh_flow, ic_density_vel_y);
sln_e.set_exact(&mesh_flow, ic_energy);
sln_c.set_exact(&mesh_concentration, ic_concentration);
prev_rho.set_exact(&mesh_flow, ic_density);
prev_rho_v_x.set_exact(&mesh_flow, ic_density_vel_x);
prev_rho_v_y.set_exact(&mesh_flow, ic_density_vel_y);
prev_e.set_exact(&mesh_flow, ic_energy);
prev_c.set_exact(&mesh_concentration, ic_concentration);
// Initialize weak formulation.
WeakForm wf(5);
// Bilinear forms coming from time discretization by explicit Euler's method.
wf.add_matrix_form(0, 0, callback(bilinear_form_time));
wf.add_matrix_form(1, 1, callback(bilinear_form_time));
wf.add_matrix_form(2, 2, callback(bilinear_form_time));
wf.add_matrix_form(3, 3, callback(bilinear_form_time));
wf.add_matrix_form(4, 4, callback(bilinear_form_time));
// Volumetric linear forms.
// Linear forms coming from the linearization by taking the Eulerian fluxes' Jacobian matrices
// from the previous time step.
// Unnecessary for FVM.
if(P_INIT_FLOW.order_h > 0 || P_INIT_FLOW.order_v > 0) {
// First flux.
wf.add_vector_form(0, callback(linear_form_0_1), HERMES_ANY, Hermes::vector<MeshFunction*>(&prev_rho_v_x));
wf.add_vector_form(1, callback(linear_form_1_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Second flux.
wf.add_vector_form(0, callback(linear_form_0_2), HERMES_ANY, Hermes::vector<MeshFunction*>(&prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
// Volumetric linear forms coming from the time discretization.
wf.add_vector_form(0, linear_form_time, linear_form_order, HERMES_ANY, &prev_rho);
wf.add_vector_form(1, linear_form_time, linear_form_order, HERMES_ANY, &prev_rho_v_x);
wf.add_vector_form(2, linear_form_time, linear_form_order, HERMES_ANY, &prev_rho_v_y);
wf.add_vector_form(3, linear_form_time, linear_form_order, HERMES_ANY, &prev_e);
wf.add_vector_form(4, callback(linear_form_time_concentration), HERMES_ANY, &prev_c);
// Surface linear forms - inner edges coming from the DG formulation.
wf.add_vector_form_surf(0, linear_form_interface_0, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, linear_form_interface_1, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, linear_form_interface_2, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, linear_form_interface_3, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Surface linear forms - inlet / outlet edges.
wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_0, linear_form_order, BDY_INLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_1, linear_form_order, BDY_INLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_2, linear_form_order, BDY_INLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_3, linear_form_order, BDY_INLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_0, linear_form_order, BDY_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_1, linear_form_order, BDY_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_2, linear_form_order, BDY_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_3, linear_form_order, BDY_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Surface linear forms - Solid wall edges.
wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_0, linear_form_order, BDY_SOLID_WALL_TOP,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_1, linear_form_order, BDY_SOLID_WALL_TOP,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_2, linear_form_order, BDY_SOLID_WALL_TOP,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_3, linear_form_order, BDY_SOLID_WALL_TOP,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_0, linear_form_order, BDY_SOLID_WALL_BOTTOM,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_1, linear_form_order, BDY_SOLID_WALL_BOTTOM,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_2, linear_form_order, BDY_SOLID_WALL_BOTTOM,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_3, linear_form_order, BDY_SOLID_WALL_BOTTOM,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Forms for concentration.
wf.add_vector_form(4, callback(linear_form_concentration_grad_grad), HERMES_ANY, &prev_c);
wf.add_vector_form(4, callback(linear_form_concentration_convective), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_c, &prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form_surf(4, callback(linear_form_concentration_inlet_outlet), BDY_INLET,
Hermes::vector<MeshFunction*>(&prev_c, &prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form_surf(4, callback(linear_form_concentration_inlet_outlet), BDY_OUTLET,
Hermes::vector<MeshFunction*>(&prev_c, &prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form_surf(4, callback(linear_form_concentration_inner_edges), H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_c, &prev_rho, &prev_rho_v_x, &prev_rho_v_y));
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e, &space_c), is_linear);
// Filters for visualization of pressure and the two components of velocity.
/*
SimpleFilter pressure(calc_pressure_func, Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter u(calc_u_func, Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter w(calc_w_func, Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter Mach_number(calc_Mach_func, Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
SimpleFilter entropy_estimate(calc_entropy_estimate_func, Hermes::vector<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
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));
VectorView vview("Velocity", new WinGeom(700, 400, 600, 300));
*/
ScalarView s1("w0", new WinGeom(0, 0, 600, 300));
ScalarView s2("w1", new WinGeom(700, 0, 600, 300));
ScalarView s3("w2", new WinGeom(0, 400, 600, 300));
ScalarView s4("w3", new WinGeom(700, 400, 600, 300));
ScalarView s5("Concentration", new WinGeom(350, 200, 600, 300));
// Iteration number.
int iteration = 0;
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Output of the approximate time derivative.
std::ofstream time_der_out("time_der");
for(t = 0.0; t < 3.0; t += TAU) {
info("---- Time step %d, time %3.5f.", iteration++, t);
bool rhs_only = (iteration == 1 ? false : true);
// Assemble stiffness matrix and rhs or just rhs.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
// Solve the matrix problem.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(), Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e, &space_c), Hermes::vector<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e, &sln_c));
else
error ("Matrix solver failed.\n");
// Copy the solutions into the previous time level ones.
prev_rho.copy(&sln_rho);
prev_rho_v_x.copy(&sln_rho_v_x);
prev_rho_v_y.copy(&sln_rho_v_y);
prev_e.copy(&sln_e);
prev_c.copy(&sln_c);
// Visualization.
/*
pressure.reinit();
u.reinit();
w.reinit();
Mach_number.reinit();
entropy_estimate.reinit();
pressure_view.show(&pressure);
entropy_production_view.show(&entropy_estimate);
Mach_number_view.show(&Mach_number);
vview.show(&u, &w);
*/
// Visualization.
if((iteration - 1) % EVERY_NTH_STEP == 0) {
// Hermes visualization.
if(HERMES_VISUALIZATION) {
s1.show(&prev_rho);
s2.show(&prev_rho_v_x);
s3.show(&prev_rho_v_y);
s4.show(&prev_e);
s5.show(&prev_c);
}
// Output solution in VTK format.
if(VTK_OUTPUT) {
Linearizer lin;
char filename[40];
sprintf(filename, "w0-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_rho, filename, "w0", false);
sprintf(filename, "w1-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_rho_v_x, filename, "w1", false);
sprintf(filename, "w2-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_rho_v_y, filename, "w2", false);
sprintf(filename, "w3-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_e, filename, "w3", false);
sprintf(filename, "concentration-%i.vtk", iteration - 1);
lin.save_solution_vtk(&prev_c, filename, "concentration", false);
}
}
}
s1.close();
s2.close();
s3.close();
s4.close();
s5.close();
time_der_out.close();
return 0;
}
int main(int argc, char* argv[])
{
/* So far the DG assembling is very slow for higher order polynomials,
so only constant functions are used here.
if(argc < 3)
error("Too few arguments in example-euler-gamm-explicit");
Ord2 P_INIT= Ord2(atoi(argv[1]), atoi(argv[2]));
*/
Ord2 P_INIT= Ord2(0, 0);
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("GAMM-channel.mesh", &mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(1, 1);
mesh.refine_element_id(1053);
mesh.refine_element_id(1054);
mesh.refine_element_id(1087);
mesh.refine_element_id(1088);
mesh.refine_element_id(1117);
mesh.refine_element_id(1118);
mesh.refine_element_id(1151);
mesh.refine_element_id(1152);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_neumann(Hermes::vector<int>(BDY_SOLID_WALL, BDY_INLET_OUTLET));
// Create L2 spaces with default shapesets.
L2Space space_rho(&mesh, &bc_types, P_INIT);
L2Space space_rho_v_x(&mesh, &bc_types, P_INIT);
L2Space space_rho_v_y(&mesh, &bc_types, P_INIT);
L2Space space_e(&mesh, &bc_types, P_INIT);
// Initialize solutions, set initial conditions.
Solution sln_rho, sln_rho_v_x, sln_rho_v_y, sln_e, prev_rho, prev_rho_v_x, prev_rho_v_y, prev_e;
sln_rho.set_exact(&mesh, ic_density);
sln_rho_v_x.set_exact(&mesh, ic_density_vel_x);
sln_rho_v_y.set_exact(&mesh, ic_density_vel_y);
sln_e.set_exact(&mesh, ic_energy);
prev_rho.set_exact(&mesh, ic_density);
prev_rho_v_x.set_exact(&mesh, ic_density_vel_x);
prev_rho_v_y.set_exact(&mesh, ic_density_vel_y);
prev_e.set_exact(&mesh, ic_energy);
// Initialize weak formulation.
WeakForm wf(4);
// Bilinear forms coming from time discretization by explicit Euler's method.
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0_time));
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1_time));
wf.add_matrix_form(2, 2, callback(bilinear_form_2_2_time));
wf.add_matrix_form(3, 3, callback(bilinear_form_3_3_time));
// Volumetric linear forms.
// Linear forms coming from the linearization by taking the Eulerian fluxes' Jacobian matrices
// from the previous time step.
// Unnecessary for FVM.
if(P_INIT.order_h > 0 || P_INIT.order_v > 0) {
// First flux.
wf.add_vector_form(0, callback(linear_form_0_1), HERMES_ANY, Hermes::vector<MeshFunction*>(&prev_rho_v_x));
wf.add_vector_form(1, callback(linear_form_1_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_first_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Second flux.
wf.add_vector_form(0, callback(linear_form_0_2), HERMES_ANY, Hermes::vector<MeshFunction*>(&prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(1, callback(linear_form_1_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(2, callback(linear_form_2_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y));
wf.add_vector_form(2, callback(linear_form_2_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_0_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_1_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_2_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form(3, callback(linear_form_3_3_second_flux), HERMES_ANY,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
}
// Volumetric linear forms coming from the time discretization.
wf.add_vector_form(0, linear_form, linear_form_order, HERMES_ANY, &prev_rho);
wf.add_vector_form(1, linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_x);
wf.add_vector_form(2, linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_y);
wf.add_vector_form(3, linear_form, linear_form_order, HERMES_ANY, &prev_e);
// Surface linear forms - inner edges coming from the DG formulation.
wf.add_vector_form_surf(0, linear_form_interface_0, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, linear_form_interface_1, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, linear_form_interface_2, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, linear_form_interface_3, linear_form_order, H2D_DG_INNER_EDGE,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Surface linear forms - inlet / outlet edges.
wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_0, linear_form_order, BDY_INLET_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_1, linear_form_order, BDY_INLET_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_2, linear_form_order, BDY_INLET_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_3, linear_form_order, BDY_INLET_OUTLET,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Surface linear forms - Solid wall edges.
wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_0, linear_form_order, BDY_SOLID_WALL,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_1, linear_form_order, BDY_SOLID_WALL,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_2, linear_form_order, BDY_SOLID_WALL,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_3, linear_form_order, BDY_SOLID_WALL,
Hermes::vector<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e));
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::vector<Space*>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), is_linear);
// If the FE problem is in fact a FV problem.
if(P_INIT.order_h == 0 && P_INIT.order_v == 0)
dp.set_fvm();
// Iteration number.
int iteration = 0;
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// For testing purposes.
double l2_norms[5][4];
for(unsigned int i = 0; i < 5; i++)
for(unsigned int j = 0; j < 4; j++)
l2_norms[i][j] = 0.0;
double point_values[5][3];
for(unsigned int i = 0; i < 5; i++)
for(unsigned int j = 0; j < 3; j++)
point_values[i][j] = 0.0;
// Calculate the special point where we will evaluate the solution.
double x = 0.75;
double y = sqrt((double)(1.-x*x)) + 0.001;
for(unsigned int time_step = 0; time_step < 5; time_step++)
{
iteration++;
bool rhs_only = (iteration == 1 ? false : true);
// Assemble stiffness matrix and rhs or just rhs.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
// Solve the matrix problem.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(), Hermes::vector<Space *>(&space_rho, &space_rho_v_x,
&space_rho_v_y, &space_e), Hermes::vector<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e));
else
error ("Matrix solver failed.\n");
// Approximate the time derivative of the solution.
if(CALC_TIME_DER) {
Adapt *adapt_for_time_der_calc = new Adapt(Hermes::vector<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e));
bool solutions_for_adapt = false;
double difference = iteration == 1 ? 0 :
adapt_for_time_der_calc->calc_err_est(Hermes::vector<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e),
Hermes::vector<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e),
(Hermes::vector<double>*) NULL, solutions_for_adapt,
HERMES_TOTAL_ERROR_ABS | HERMES_ELEMENT_ERROR_ABS) / TAU;
delete adapt_for_time_der_calc;
}
// Determine the time step according to the CFL condition.
// Only mean values on an element of each solution component are taken into account.
double *solution_vector = solver->get_solution();
double min_condition = 0;
Element *e;
for (int _id = 0, _max = mesh.get_max_element_id(); _id < _max; _id++) \
if (((e) = mesh.get_element_fast(_id))->used) \
if ((e)->active) {
AsmList al;
space_rho.get_element_assembly_list(e, &al);
double rho = solution_vector[al.dof[0]];
space_rho_v_x.get_element_assembly_list(e, &al);
double v1 = solution_vector[al.dof[0]] / rho;
space_rho_v_y.get_element_assembly_list(e, &al);
double v2 = solution_vector[al.dof[0]] / rho;
space_e.get_element_assembly_list(e, &al);
double energy = solution_vector[al.dof[0]];
double condition = e->get_area() / (std::sqrt(v1*v1 + v2*v2) + calc_sound_speed(rho, rho*v1, rho*v2, energy));
if(condition < min_condition || min_condition == 0.)
min_condition = condition;
}
if(TAU > min_condition)
TAU = min_condition;
if(TAU < min_condition * 0.9)
TAU = min_condition;
// Storing the testing values.
for(unsigned int j = 0; j < 4; j++)
for(unsigned int k = j*space_rho.get_num_dofs(); k < (j+1)*space_rho.get_num_dofs(); k++)
l2_norms[time_step][j] += solver->get_solution()[k];
point_values[time_step][0] = sln_rho_v_x.get_pt_value(0.5, 0.001);
point_values[time_step][1] = sln_rho_v_x.get_pt_value(x, y);
point_values[time_step][2] = sln_rho_v_x.get_pt_value(1.5, 0.001);
// Copy the solutions into the previous time level ones.
prev_rho.copy(&sln_rho);
prev_rho_v_x.copy(&sln_rho_v_x);
prev_rho_v_y.copy(&sln_rho_v_y);
prev_e.copy(&sln_e);
}
bool okay = true;
switch(P_INIT.order_h* 10 + P_INIT.order_v) {
case 0:
if(std::abs(l2_norms[0][0] - 888.0) > 1E-8)
okay = false;
if(std::abs(l2_norms[0][1] - 1110) > 1E-8)
okay = false;
if(std::abs(l2_norms[0][2]) > 1E-8)
okay = false;
if(std::abs(l2_norms[0][3] - 6243.75) > 1E-8)
okay = false;
if(std::abs(l2_norms[1][0] - 887.99997637865545) > 1E-8)
okay = false;
if(std::abs(l2_norms[1][1] - 1109.9997956458228) > 1E-8)
okay = false;
if(std::abs(l2_norms[1][2] - 3.1927018090871903e-008) > 1E-8)
okay = false;
if(std::abs(l2_norms[1][3] - 6243.7496921971369) > 1E-8)
okay = false;
if(std::abs(l2_norms[2][0] - 887.99993429457072) > 1E-8)
okay = false;
if(std::abs(l2_norms[2][1] - 1109.9994322038613) > 1E-8)
okay = false;
if(std::abs(l2_norms[2][2] + 5.3556469633245445e-008) > 1E-8)
okay = false;
if(std::abs(l2_norms[2][3] - 6243.7491437826511) > 1E-8)
okay = false;
if(std::abs(l2_norms[3][0] - 887.99987376550200) > 1E-8)
okay = false;
if(std::abs(l2_norms[3][1] - 1109.9989102977672) > 1E-8)
okay = false;
if(std::abs(l2_norms[3][2] + 3.6958140470412712e-007) > 1E-8)
okay = false;
if(std::abs(l2_norms[3][3] - 6243.7483549661320) > 1E-8)
okay = false;
if(std::abs(l2_norms[4][0] - 887.99979481320088) > 1E-8)
okay = false;
if(std::abs(l2_norms[4][1] - 1109.9982305630808) > 1E-8)
okay = false;
if(std::abs(l2_norms[4][2] + 1.0303296924184822e-006) > 1E-8)
okay = false;
if(std::abs(l2_norms[4][3] - 6243.7473260085462) > 1E-8)
okay = false;
// points
if(std::abs(point_values[0][0] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[0][1] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[0][2] - 1.2459744738974898) > 1E-8)
okay = false;
if(std::abs(point_values[1][0] - 1.2499951035194972) > 1E-8)
okay = false;
if(std::abs(point_values[1][1] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[1][2] - 1.2428402692519325) > 1E-8)
okay = false;
if(std::abs(point_values[2][0] - 1.2499864002215795) > 1E-8)
okay = false;
if(std::abs(point_values[2][1] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[2][2] - 1.2397180160697001) > 1E-8)
okay = false;
if(std::abs(point_values[3][0] - 1.2499739085927257) > 1E-8)
okay = false;
if(std::abs(point_values[3][1] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[3][2] - 1.2366079101139087) > 1E-8)
okay = false;
if(std::abs(point_values[4][0] - 1.2499576472516911) > 1E-8)
okay = false;
if(std::abs(point_values[4][1] - 1.25) > 1E-8)
okay = false;
if(std::abs(point_values[4][2] - 1.2335101392959738) > 1E-8)
okay = false;
break;
}
if (okay) { // ndofs was 908 at the time this test was created
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}