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[]) { /* 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; } }