int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("domain.mesh", &mesh);
// Initial mesh refinements.
mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_OBSTACLE, 4, false);
mesh.refine_towards_boundary(BDY_TOP, 4, true); // '4' is the number of levels,
mesh.refine_towards_boundary(BDY_BOTTOM, 4, true); // 'true' stands for anisotropic refinements.
// Initialize boundary conditions.
EssentialBCNonConst bc_left_vel_x(BDY_LEFT, VEL_INLET, H, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_other_vel_x(Hermes::vector<std::string>(BDY_BOTTOM, BDY_TOP, BDY_OBSTACLE), 0.0);
EssentialBCs<double> bcs_vel_x(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_left_vel_x, &bc_other_vel_x));
DefaultEssentialBCConst<double> bc_vel_y(Hermes::vector<std::string>(BDY_LEFT, BDY_BOTTOM, BDY_TOP, BDY_OBSTACLE), 0.0);
EssentialBCs<double> bcs_vel_y(&bc_vel_y);
// Spaces for velocity components and pressure.
H1Space<double> xvel_space(&mesh, &bcs_vel_x, P_INIT_VEL);
H1Space<double> yvel_space(&mesh, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space<double> p_space(&mesh, P_INIT_PRESSURE);
#else
H1Space<double> p_space(&mesh, P_INIT_PRESSURE);
#endif
// Calculate and report the number of degrees of freedom.
int ndof = Space<double>::get_num_dofs(Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space));
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
// Solutions for the Newton's iteration and time stepping.
info("Setting initial conditions.");
ZeroSolution xvel_prev_time(&mesh);
ZeroSolution yvel_prev_time(&mesh);
ZeroSolution p_prev_time(&mesh);
// Initialize weak formulation.
WeakForm<double>* wf;
if (NEWTON)
wf = new WeakFormNSNewton(STOKES, RE, TAU, &xvel_prev_time, &yvel_prev_time);
else
wf = new WeakFormNSSimpleLinearization(STOKES, RE, TAU, &xvel_prev_time, &yvel_prev_time);
// Initialize the FE problem.
DiscreteProblem<double> dp(wf, Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space));
// 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);
// 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);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
double* coeff_vec = new double[Space<double>::get_num_dofs(Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space))];
if (NEWTON)
{
info("Projecting initial condition to obtain initial vector for the Newton's method.");
OGProjection<double>::project_global(Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<MeshFunction<double>*>(&xvel_prev_time, &yvel_prev_time, &p_prev_time),
coeff_vec, matrix_solver_type,
Hermes::vector<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm));
}
// 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;
info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
if (current_time <= STARTUP_TIME) {
info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space), current_time);
}
if (NEWTON)
{
// Perform Newton's iteration.
info("Solving nonlinear problem:");
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
try
{
newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
};
// Update previous time level solutions.
Solution<double>::vector_to_solutions(coeff_vec, Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<Solution<double>*>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
}
else
{
// Linear solve.
info("Assembling and solving linear problem.");
dp.assemble(matrix, rhs, false);
if(solver->solve())
Solution<double>::vector_to_solutions(solver->get_sln_vector(),
Hermes::vector<Space<double>*>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<Solution<double>*>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
else
error ("Matrix solver failed.\n");
}
// 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, HERMES_EPS_LOW);
sprintf(title, "Pressure, time %g", current_time);
pview.set_title(title);
pview.show(&p_prev_time);
}
delete [] coeff_vec;
delete matrix;
delete rhs;
delete solver;
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
Hermes2D hermes_2D;
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("../domain-excentric.mesh", &mesh);
//mloader.load("../domain-concentric.mesh", &mesh);
// Initial mesh refinements.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_INNER, INIT_BDY_REF_NUM_INNER, false); // true for anisotropic refinements
mesh.refine_towards_boundary(BDY_OUTER, INIT_BDY_REF_NUM_OUTER, false); // false for isotropic refinements
// Initialize boundary conditions.
EssentialBCNonConstX bc_inner_vel_x(BDY_INNER, VEL, STARTUP_TIME);
EssentialBCNonConstY bc_inner_vel_y(BDY_INNER, VEL, STARTUP_TIME);
DefaultEssentialBCConst bc_outer_vel(BDY_OUTER, 0.0);
EssentialBCs bcs_vel_x(Hermes::vector<EssentialBoundaryCondition *>(&bc_inner_vel_x, &bc_outer_vel));
EssentialBCs bcs_vel_y(Hermes::vector<EssentialBoundaryCondition *>(&bc_inner_vel_y, &bc_outer_vel));
EssentialBCs bcs_pressure;
// Spaces for velocity components and pressure.
H1Space xvel_space(&mesh, &bcs_vel_x, P_INIT_VEL);
H1Space yvel_space(&mesh, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#else
H1Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#endif
// Calculate and report the number of degrees of freedom.
int ndof = Space::get_num_dofs(Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space));
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
// Solutions for the Newton's iteration and time stepping.
Solution xvel_prev_time, yvel_prev_time, p_prev_time;
xvel_prev_time.set_zero(&mesh);
yvel_prev_time.set_zero(&mesh);
p_prev_time.set_zero(&mesh);
// Initialize weak formulation.
WeakForm* wf;
if (NEWTON)
wf = new WeakFormNSNewton(STOKES, RE, TAU, &xvel_prev_time, &yvel_prev_time);
else
wf = new WeakFormNSSimpleLinearization(STOKES, RE, TAU, &xvel_prev_time, &yvel_prev_time);
// Initialize the FE problem.
bool is_linear;
if (NEWTON) is_linear = false;
else is_linear = true;
DiscreteProblem dp(wf, Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space), is_linear);
// 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);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[Space::get_num_dofs(Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space))];
if (NEWTON) {
OGProjection::project_global(Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<MeshFunction*>(&xvel_prev_time, &yvel_prev_time, &p_prev_time),
coeff_vec, matrix_solver,
Hermes::vector<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm));
}
// 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;
// Update time-dependent essential BCs.
Space::update_essential_bc_values(Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space), current_time);
if (NEWTON)
{
// Perform Newton's iteration.
bool verbose = false;
if (!hermes_2D.solve_newton(coeff_vec, &dp, solver, matrix, rhs,
NEWTON_TOL, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
// Update previous time level solutions.
Solution::vector_to_solutions(coeff_vec, Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<Solution *>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
}
else {
// Linear solve.
dp.assemble(matrix, rhs, false);
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(),
Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::vector<Solution *>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
else
error ("Matrix solver failed.\n");
}
}
// Clean up.
delete [] coeff_vec;
delete matrix;
delete rhs;
delete solver;
info("Coordinate ( -0.7, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(-0.7, 0.1));
info("Coordinate ( 0.65, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.65, 0.0));
info("Coordinate ( 0.7, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.7, 0.0));
info("Coordinate ( 0.9, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.9, 0.0));
info("Coordinate ( 1.1, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(1.1, 0.0));
info("Coordinate ( -0.7, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(-0.7, 0.1));
info("Coordinate ( 0.65, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.65, 0.0));
info("Coordinate ( 0.7, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.7, 0.0));
info("Coordinate ( 0.9, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.9, 0.0));
info("Coordinate ( 1.1, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(1.1, 0.0));
int success = 1;
double eps = 1e-5;
if (fabs(xvel_prev_time.get_pt_value(-0.7, 0.1) - (0.003199)) > eps) {
printf("Coordinate ( -0.7, 0.1) xvel value = %lf\n", xvel_prev_time.get_pt_value(-0.7, 0.1));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(0.65, 0.0) - (-0.001314)) > eps) {
printf("Coordinate ( 0.65, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.65, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(0.7, 0.0) - (-0.001888)) > eps) {
printf("Coordinate ( 0.7, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.7, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(0.9, 0.0) - (-0.001262)) > eps) {
printf("Coordinate ( 0.9, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.9, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(1.1, 0.0) - (-0.000218)) > eps) {
printf("Coordinate ( 1.1, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(1.1, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(-0.7, 0.1) - (0.014744)) > eps) {
printf("Coordinate ( -0.7, 0.1) yvel value = %lf\n", yvel_prev_time.get_pt_value(-0.7, 0.1));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.65, 0.0) - (-0.033332)) > eps) {
printf("Coordinate ( 0.65, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.65, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.7, 0.0) - (-0.012353)) > eps) {
printf("Coordinate ( 0.7, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.7, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.9, 0.0) - (-0.001691)) > eps) {
printf("Coordinate ( 0.9, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.9, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(1.1, 0.0) - (-0.000986)) > eps) {
printf("Coordinate ( 1.1, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(1.1, 0.0));
success = 0;
}
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
Hermes2D hermes_2D;
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain-excentric.mesh", &mesh);
//mloader.load("domain-concentric.mesh", &mesh);
// Initial mesh refinements.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary("Inner", INIT_BDY_REF_NUM_INNER, false); // true for anisotropic refinements
mesh.refine_towards_boundary("Outer", INIT_BDY_REF_NUM_OUTER, false); // false for isotropic refinements
// Initialize boundary conditions.
EssentialBCNonConstX bc_inner_vel_x(std::string("Inner"), VEL, STARTUP_TIME);
EssentialBCNonConstY bc_inner_vel_y(std::string("Inner"), VEL, STARTUP_TIME);
DefaultEssentialBCConst bc_outer_vel(std::string("Outer"), 0.0);
EssentialBCs bcs_vel_x(Hermes::vector<EssentialBoundaryCondition *>(&bc_inner_vel_x, &bc_outer_vel));
EssentialBCs bcs_vel_y(Hermes::vector<EssentialBoundaryCondition *>(&bc_inner_vel_y, &bc_outer_vel));
EssentialBCs bcs_pressure;
// Spaces for velocity components and pressure.
H1Space xvel_space(&mesh, &bcs_vel_x, P_INIT_VEL);
H1Space yvel_space(&mesh, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#else
H1Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#endif
Hermes::vector<Space *> spaces = Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space);
// Calculate and report the number of degrees of freedom.
int ndof = Space::get_num_dofs(spaces);
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
// Solutions for the Newton's iteration and time stepping.
info("Setting initial conditions.");
Solution xvel_prev_time, yvel_prev_time, p_prev_time;
xvel_prev_time.set_zero(&mesh);
yvel_prev_time.set_zero(&mesh);
p_prev_time.set_zero(&mesh);
Hermes::vector<Solution*> slns = Hermes::vector<Solution*>(&xvel_prev_time, &yvel_prev_time,
&p_prev_time);
// Initialize weak formulation.
WeakForm* wf = new WeakFormNSNewton(STOKES, RE, TAU, &xvel_prev_time, &yvel_prev_time);
// Initialize the FE problem.
DiscreteProblem dp(wf, spaces);
// 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);
// Initialize views.
VectorView vview("velocity [m/s]", new WinGeom(0, 0, 600, 500));
ScalarView pview("pressure [Pa]", new WinGeom(610, 0, 600, 500));
//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);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[Space::get_num_dofs(spaces)];
// Newton's vector is set to zero (no OG projection needed).
memset(coeff_vec, 0, ndof * sizeof(double));
/*
// This can be used for more complicated initial conditions.
info("Projecting initial condition to obtain initial vector for the Newton's method.");
OGProjection::project_global(spaces, slns, coeff_vec, matrix_solver,
Hermes::vector<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm));
*/
// 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;
info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
info("Updating time-dependent essential BC.");
Space::update_essential_bc_values(Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space), current_time);
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
bool jacobian_changed = true;
if (!hermes_2D.solve_newton(coeff_vec, &dp, solver, matrix, rhs, jacobian_changed,
NEWTON_TOL, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
// Update previous time level solutions.
Solution::vector_to_solutions(coeff_vec, spaces, slns);
// 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);
}
// Clean up.
delete [] coeff_vec;
delete matrix;
delete rhs;
delete solver;
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
Hermes2D hermes_2D;
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Initial mesh refinements.
for (int i=0; i < 4; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(HERMES_ANY, 4);
// Initialize boundary conditions.
DefaultEssentialBCConst zero_vel_bc_x_brl(Hermes::vector<std::string>("Bottom", "Right", "Left"), 0.0);
DefaultEssentialBCConst vel_bc_x_top(Hermes::vector<std::string>("Top"), XVEL_TOP);
EssentialBCs bcs_vel_x(Hermes::vector<EssentialBoundaryCondition*>(&vel_bc_x_top, &zero_vel_bc_x_brl));
DefaultEssentialBCConst zero_vel_bc_y(Hermes::vector<std::string>("Bottom", "Right", "Top", "Left"), 0.0);
EssentialBCs bcs_vel_y(&zero_vel_bc_y);
EssentialBCs bcs_pressure;
// Spaces for velocity components and pressure.
H1Space xvel_space(&mesh, &bcs_vel_x, P_INIT_VEL);
H1Space yvel_space(&mesh, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#else
H1Space p_space(&mesh, &bcs_pressure, P_INIT_PRESSURE);
#endif
Hermes::vector<Space *> spaces = Hermes::vector<Space *>(&xvel_space, &yvel_space, &p_space);
// Calculate and report the number of degrees of freedom.
int ndof = Space::get_num_dofs(spaces);
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
ProjNormType t_proj_norm = HERMES_H1_NORM;
// Solutions for the Newton's iteration and time stepping.
info("Setting initial conditions.");
Solution xvel_prev_time, yvel_prev_time, p_prev_time;
xvel_prev_time.set_zero(&mesh);
yvel_prev_time.set_zero(&mesh);
p_prev_time.set_zero(&mesh);
Hermes::vector<Solution*> slns = Hermes::vector<Solution*>(&xvel_prev_time, &yvel_prev_time,
&p_prev_time);
// Initialize weak formulation.
WeakForm* wf = new WeakFormDrivenCavity(Re, "Top", time_step,
&xvel_prev_time, &yvel_prev_time);
// Initialize the FE problem.
DiscreteProblem dp(wf, spaces);
// 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);
// Initialize views.
VectorView vview("velocity", new WinGeom(0, 0, 400, 400));
ScalarView pview("pressure", new WinGeom(410, 0, 400, 400));
//vview.set_min_max_range(0, 1.6);
vview.fix_scale_width(80);
pview.fix_scale_width(80);
pview.show_mesh(true);
// Project the initial condition on the FE space to obtain initial
// coefficient vector for the Newton's method.
scalar* coeff_vec = new scalar[ndof];
// Newton's vector is set to zero (no OG projection needed).
memset(coeff_vec, 0, ndof * sizeof(double));
/*
// This can be used for more complicated initial conditions.
info("Projecting initial condition to obtain initial vector for the Newton's method.");
OGProjection::project_global(spaces, slns, coeff_vec, matrix_solver,
Hermes::vector<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm, t_proj_norm));
*/
// Time-stepping loop:
char title[100];
double current_time = 0;
int num_time_steps = T_FINAL / time_step;
for (int ts = 1; ts <= num_time_steps; ts++)
{
info("---- Time step %d, time = %g:", ts, current_time);
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
bool jacobian_changed = true;
if (!hermes_2D.solve_newton(coeff_vec, &dp, solver, matrix, rhs, jacobian_changed,
NEWTON_TOL, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
// Update previous time level solutions.
Solution::vector_to_solutions(coeff_vec, spaces, slns);
// 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);
// Update current time.
current_time += time_step;
}
// Clean up.
delete [] coeff_vec;
delete matrix;
delete rhs;
delete solver;
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh_whole_domain, mesh_with_hole;
Hermes::vector<Mesh*> meshes (&mesh_whole_domain, &mesh_with_hole);
MeshReaderH2DXML mloader;
mloader.load("domain.xml", meshes);
// Temperature mesh: Initial uniform mesh refinements in graphite.
meshes[0]->refine_by_criterion(element_in_graphite, INIT_REF_NUM_TEMPERATURE_GRAPHITE);
// Temperature mesh: Initial uniform mesh refinements in fluid.
meshes[0]->refine_by_criterion(element_in_fluid, INIT_REF_NUM_TEMPERATURE_FLUID);
// Fluid mesh: Initial uniform mesh refinements.
for(int i = 0; i < INIT_REF_NUM_FLUID; i++)
meshes[1]->refine_all_elements();
// Initial refinements towards boundary of graphite.
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_towards_boundary("Inner Wall", INIT_REF_NUM_BDY_GRAPHITE);
// Initial refinements towards the top and bottom edges.
for(unsigned int meshes_i = 0; meshes_i < meshes.size(); meshes_i++)
meshes[meshes_i]->refine_towards_boundary("Outer Wall", INIT_REF_NUM_BDY_WALL);
/* View both meshes. */
MeshView m1("Mesh for temperature"), m2("Mesh for fluid");
m1.show(&mesh_whole_domain);
m2.show(&mesh_with_hole);
// Initialize boundary conditions.
EssentialBCNonConst bc_inlet_vel_x("Inlet", VEL_INLET, H, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_other_vel_x(Hermes::vector<std::string>("Outer Wall", "Inner Wall"), 0.0);
EssentialBCs<double> bcs_vel_x(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_inlet_vel_x, &bc_other_vel_x));
DefaultEssentialBCConst<double> bc_vel_y(Hermes::vector<std::string>("Inlet", "Outer Wall", "Inner Wall"), 0.0);
EssentialBCs<double> bcs_vel_y(&bc_vel_y);
EssentialBCs<double> bcs_pressure;
DefaultEssentialBCConst<double> bc_temperature(Hermes::vector<std::string>("Outer Wall", "Inlet"), 20.0);
EssentialBCs<double> bcs_temperature(&bc_temperature);
// Spaces for velocity components, pressure and temperature.
H1Space<double> xvel_space(&mesh_with_hole, &bcs_vel_x, P_INIT_VEL);
H1Space<double> yvel_space(&mesh_with_hole, &bcs_vel_y, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space<double> p_space(&mesh_with_hole, P_INIT_PRESSURE);
#else
H1Space<double> p_space(&mesh_with_hole, &bcs_pressure, P_INIT_PRESSURE);
#endif
H1Space<double> temperature_space(&mesh_whole_domain, &bcs_temperature, P_INIT_TEMPERATURE);
Hermes::vector<Space<double> *> all_spaces(&xvel_space,
&yvel_space, &p_space, &temperature_space);
Hermes::vector<const Space<double> *> all_spaces_const(&xvel_space,
&yvel_space, &p_space, &temperature_space);
// Calculate and report the number of degrees of freedom.
int ndof = Space<double>::get_num_dofs(Hermes::vector<const Space<double> *>(&xvel_space,
&yvel_space, &p_space, &temperature_space));
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
ProjNormType temperature_proj_norm = HERMES_H1_NORM;
Hermes::vector<ProjNormType> all_proj_norms = Hermes::vector<ProjNormType>(vel_proj_norm,
vel_proj_norm, p_proj_norm, temperature_proj_norm);
// Initial conditions and such.
info("Setting initial conditions.");
ZeroSolution xvel_prev_time(&mesh_with_hole), yvel_prev_time(&mesh_with_hole), p_prev_time(&mesh_with_hole);
CustomInitialConditionTemperature temperature_init_cond(&mesh_whole_domain, HOLE_MID_X, HOLE_MID_Y,
0.5*OBSTACLE_DIAMETER, TEMPERATURE_INIT_FLUID, TEMPERATURE_INIT_GRAPHITE);
Solution<double> temperature_prev_time;
Hermes::vector<Solution<double> *> all_solutions = Hermes::vector<Solution<double> *>(&xvel_prev_time,
&yvel_prev_time, &p_prev_time, &temperature_prev_time);
Hermes::vector<MeshFunction<double> *> all_meshfns = Hermes::vector<MeshFunction<double> *>(&xvel_prev_time,
&yvel_prev_time, &p_prev_time, &temperature_init_cond);
// Project all initial conditions on their FE spaces to obtain aninitial
// coefficient vector for the Newton's method. We use local projection
// to avoid oscillations in temperature on the graphite-fluid interface
// FIXME - currently the LocalProjection only does the lowest-order part (linear
// interpolation) at the moment. Higher-order part needs to be added.
double* coeff_vec = new double[ndof];
info("Projecting initial condition to obtain initial vector for the Newton's method.");
//OGProjection<double>::project_global(all_spaces, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);
LocalProjection<double>::project_local(all_spaces_const, all_meshfns, coeff_vec, matrix_solver, all_proj_norms);
// Translate the solution vector back to Solutions. This is needed to replace
// the discontinuous initial condition for temperature_prev_time with its projection.
Solution<double>::vector_to_solutions(coeff_vec, all_spaces_const, all_solutions);
// Calculate Reynolds number.
double reynolds_number = VEL_INLET * OBSTACLE_DIAMETER / KINEMATIC_VISCOSITY_FLUID;
info("RE = %g", reynolds_number);
if (reynolds_number < 1e-8) error("Re == 0 will not work - the equations use 1/Re.");
// Initialize weak formulation.
CustomWeakFormHeatAndFlow wf(STOKES, reynolds_number, time_step, &xvel_prev_time, &yvel_prev_time, &temperature_prev_time,
HEAT_SOURCE_GRAPHITE, SPECIFIC_HEAT_GRAPHITE, SPECIFIC_HEAT_FLUID, RHO_GRAPHITE, RHO_FLUID,
THERMAL_CONDUCTIVITY_GRAPHITE, THERMAL_CONDUCTIVITY_FLUID, SIMPLE_TEMPERATURE_ADVECTION);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, all_spaces_const);
// Initialize the Newton solver.
NewtonSolver<double> newton(&dp, matrix_solver);
// Initialize views.
Views::VectorView vview("velocity [m/s]", new Views::WinGeom(0, 0, 700, 360));
Views::ScalarView pview("pressure [Pa]", new Views::WinGeom(0, 415, 700, 350));
Views::ScalarView tempview("temperature [C]", new Views::WinGeom(0, 795, 700, 350));
//vview.set_min_max_range(0, 0.5);
vview.fix_scale_width(80);
//pview.set_min_max_range(-0.9, 1.0);
pview.fix_scale_width(80);
pview.show_mesh(false);
tempview.fix_scale_width(80);
tempview.show_mesh(false);
// Time-stepping loop:
char title[100];
int num_time_steps = T_FINAL / time_step;
double current_time = 0.0;
for (int ts = 1; ts <= num_time_steps; ts++)
{
current_time += time_step;
info("---- Time step %d, time = %g:", ts, current_time);
// Update time-dependent essential BCs.
if (current_time <= STARTUP_TIME)
{
info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(Hermes::vector<Space<double> *>(&xvel_space, &yvel_space, &p_space,
&temperature_space), current_time);
}
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
// Perform Newton's iteration and translate the resulting coefficient vector into previous time level solutions.
newton.set_verbose_output(verbose);
try
{
newton.solve(coeff_vec, NEWTON_TOL, NEWTON_MAX_ITER);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
};
{
Hermes::vector<Solution<double> *> tmp(&xvel_prev_time, &yvel_prev_time, &p_prev_time, &temperature_prev_time);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), Hermes::vector<const Space<double> *>(&xvel_space,
&yvel_space, &p_space, &temperature_space), tmp);
}
// Show the solution at the end of time step.
sprintf(title, "Velocity [m/s], time %g s", current_time);
vview.set_title(title);
vview.show(&xvel_prev_time, &yvel_prev_time);
sprintf(title, "Pressure [Pa], time %g s", current_time);
pview.set_title(title);
pview.show(&p_prev_time);
sprintf(title, "Temperature [C], time %g s", current_time);
tempview.set_title(title);
tempview.show(&temperature_prev_time, Views::HERMES_EPS_HIGH);
}
delete [] coeff_vec;
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain-excentric.mesh", mesh);
//mloader.load("domain-concentric.mesh", mesh);
// Initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++)
mesh->refine_all_elements();
// Use 'true' for anisotropic refinements.
mesh->refine_towards_boundary("Inner", INIT_BDY_REF_NUM_INNER, false);
// Use 'false' for isotropic refinements.
mesh->refine_towards_boundary("Outer", INIT_BDY_REF_NUM_OUTER, false);
// Initialize boundary conditions.
EssentialBCNonConstX bc_inner_vel_x(std::string("Inner"), VEL, STARTUP_TIME);
EssentialBCNonConstY bc_inner_vel_y(std::string("Inner"), VEL, STARTUP_TIME);
DefaultEssentialBCConst<double> bc_outer_vel(std::string("Outer"), 0.0);
EssentialBCs<double> bcs_vel_x({ &bc_inner_vel_x, &bc_outer_vel });
EssentialBCs<double> bcs_vel_y({ &bc_inner_vel_y, &bc_outer_vel });
// Spaces for velocity components and pressure.
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 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 views.
VectorView vview("velocity [m/s]", new WinGeom(0, 0, 600, 500));
ScalarView pview("pressure [Pa]", new WinGeom(610, 0, 600, 500));
//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);
// Initialize the FE problem.
Hermes::Hermes2D::NewtonSolver<double> newton(wf, spaces);
newton.set_verbose_output(true);
newton.set_max_allowed_iterations(NEWTON_MAX_ITER);
newton.set_tolerance(NEWTON_TOL, Hermes::Solvers::ResidualNormAbsolute);
// 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.
Hermes::Mixins::Loggable::Static::info("Updating time-dependent essential BC.");
Space<double>::update_essential_bc_values(spaces, current_time);
// Perform Newton's iteration.
Hermes::Mixins::Loggable::Static::info("Solving nonlinear problem:");
try
{
newton.solve();
}
catch (Hermes::Exceptions::Exception e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
};
// Update previous time level solutions.
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, { xvel_prev_time, yvel_prev_time, p_prev_time });
// 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;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain-excentric.mesh", &mesh);
//mloader.load("domain-concentric.mesh", &mesh);
// Initial mesh refinements.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_INNER, INIT_BDY_REF_NUM_INNER, false); // true for anisotropic refinements
mesh.refine_towards_boundary(BDY_OUTER, INIT_BDY_REF_NUM_OUTER, false); // false for isotropic refinements
// Enter boundary markers for x-velocity and y-velocity.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::Tuple<int>(BDY_INNER, BDY_OUTER));
BCTypes bc_types_p;
bc_types_p.add_bc_none(Hermes::Tuple<int>(BDY_INNER, BDY_OUTER));
// Enter Dirichlet boundary values.
BCValues bc_values_xvel(&TIME);
bc_values_xvel.add_timedep_function(BDY_INNER, essential_bc_values_xvel);
bc_values_xvel.add_zero(BDY_OUTER);
BCValues bc_values_yvel(&TIME);
bc_values_yvel.add_timedep_function(BDY_INNER, essential_bc_values_yvel);
bc_values_yvel.add_zero(BDY_OUTER);
// Create spaces with default shapesets.
H1Space xvel_space(&mesh, &bc_types, &bc_values_xvel, P_INIT_VEL);
H1Space yvel_space(&mesh, &bc_types, &bc_values_yvel, P_INIT_VEL);
#ifdef PRESSURE_IN_L2
L2Space p_space(&mesh, P_INIT_PRESSURE);
#else
H1Space p_space(&mesh, &bc_types_p, P_INIT_PRESSURE);
#endif
// Calculate and report the number of degrees of freedom.
int ndof = Space::get_num_dofs(Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space));
info("ndof = %d.", ndof);
// Define projection norms.
ProjNormType vel_proj_norm = HERMES_H1_NORM;
#ifdef PRESSURE_IN_L2
ProjNormType p_proj_norm = HERMES_L2_NORM;
#else
ProjNormType p_proj_norm = HERMES_H1_NORM;
#endif
// Solutions for the Newton's iteration and time stepping.
info("Setting initial conditions.");
Solution xvel_prev_time, yvel_prev_time, p_prev_time;
xvel_prev_time.set_zero(&mesh);
yvel_prev_time.set_zero(&mesh);
p_prev_time.set_zero(&mesh);
// Initialize weak formulation.
WeakForm wf(3);
if (NEWTON) {
wf.add_matrix_form(0, 0, callback(bilinear_form_sym_0_0_1_1), HERMES_SYM);
wf.add_matrix_form(0, 0, callback(newton_bilinear_form_unsym_0_0), HERMES_NONSYM, HERMES_ANY);
wf.add_matrix_form(0, 1, callback(newton_bilinear_form_unsym_0_1), HERMES_NONSYM, HERMES_ANY);
wf.add_matrix_form(0, 2, callback(bilinear_form_unsym_0_2), HERMES_ANTISYM);
wf.add_matrix_form(1, 0, callback(newton_bilinear_form_unsym_1_0), HERMES_NONSYM, HERMES_ANY);
wf.add_matrix_form(1, 1, callback(bilinear_form_sym_0_0_1_1), HERMES_SYM);
wf.add_matrix_form(1, 1, callback(newton_bilinear_form_unsym_1_1), HERMES_NONSYM, HERMES_ANY);
wf.add_matrix_form(1, 2, callback(bilinear_form_unsym_1_2), HERMES_ANTISYM);
wf.add_vector_form(0, callback(newton_F_0), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&xvel_prev_time, &yvel_prev_time));
wf.add_vector_form(1, callback(newton_F_1), HERMES_ANY,
Hermes::Tuple<MeshFunction*>(&xvel_prev_time, &yvel_prev_time));
wf.add_vector_form(2, callback(newton_F_2), HERMES_ANY);
}
else {
wf.add_matrix_form(0, 0, callback(bilinear_form_sym_0_0_1_1), HERMES_SYM);
wf.add_matrix_form(0, 0, callback(simple_bilinear_form_unsym_0_0_1_1),
HERMES_NONSYM, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&xvel_prev_time, &yvel_prev_time));
wf.add_matrix_form(1, 1, callback(bilinear_form_sym_0_0_1_1), HERMES_SYM);
wf.add_matrix_form(1, 1, callback(simple_bilinear_form_unsym_0_0_1_1),
HERMES_NONSYM, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&xvel_prev_time, &yvel_prev_time));
wf.add_matrix_form(0, 2, callback(bilinear_form_unsym_0_2), HERMES_ANTISYM);
wf.add_matrix_form(1, 2, callback(bilinear_form_unsym_1_2), HERMES_ANTISYM);
wf.add_vector_form(0, callback(simple_linear_form), HERMES_ANY, &xvel_prev_time);
wf.add_vector_form(1, callback(simple_linear_form), HERMES_ANY, &yvel_prev_time);
}
// Project initial conditions on FE spaces to obtain initial coefficient
// vector for the Newton's method.
scalar* coeff_vec = new scalar[Space::get_num_dofs(Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space))];
if (NEWTON) {
info("Projecting initial conditions to obtain initial vector for the Newton's method.");
OGProjection::project_global(Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::Tuple<MeshFunction*>(&xvel_prev_time, &yvel_prev_time, &p_prev_time),
coeff_vec, matrix_solver, Hermes::Tuple<ProjNormType>(vel_proj_norm, vel_proj_norm, p_proj_norm));
}
// Time-stepping loop:
char title[100];
int num_time_steps = T_FINAL / TAU;
for (int ts = 1; ts <= num_time_steps; ts++)
{
TIME += TAU;
info("---- Time step %d, time = %g:", ts, TIME);
// Update time-dependent essential BC are used.
if (TIME <= STARTUP_TIME) {
info("Updating time-dependent essential BC.");
update_essential_bc_values(Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space));
}
if (NEWTON)
{
info("Performing Newton's method.");
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space), is_linear);
// 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);
// Perform Newton's iteration.
info("Solving nonlinear problem:");
bool verbose = true;
if (!solve_newton(coeff_vec, &dp, solver, matrix, rhs,
NEWTON_TOL, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the actual solutions.
Solution::vector_to_solutions(coeff_vec, Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::Tuple<Solution *>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
// Cleanup.
delete matrix;
delete rhs;
delete solver;
}
else {
// Linear solve.
info("Assembling and solving linear problem.");
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space), is_linear);
// 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);
dp.assemble(matrix, rhs);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(), Hermes::Tuple<Space *>(&xvel_space, &yvel_space, &p_space),
Hermes::Tuple<Solution *>(&xvel_prev_time, &yvel_prev_time, &p_prev_time));
else
error ("Matrix solver failed.\n");
}
}
// Clean up.
delete [] coeff_vec;
info("Coordinate ( 0.1, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.1, 0.0));
info("Coordinate ( 0.5, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.5, 0.0));
info("Coordinate ( 0.9, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(0.9, 0.0));
info("Coordinate ( 1.3, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(1.3, 0.0));
info("Coordinate ( 1.7, 0.0) xvel value = %lf", xvel_prev_time.get_pt_value(1.7, 0.0));
info("Coordinate ( 0.1, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.1, 0.0));
info("Coordinate ( 0.5, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.5, 0.0));
info("Coordinate ( 0.9, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(0.9, 0.0));
info("Coordinate ( 1.3, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(1.3, 0.0));
info("Coordinate ( 1.7, 0.0) yvel value = %lf", yvel_prev_time.get_pt_value(1.7, 0.0));
int success = 1;
double eps = 1e-5;
if (fabs(xvel_prev_time.get_pt_value(0.1, 0.0) - (0.000000)) > eps) {
printf("Coordinate ( 0.1, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.1, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(0.5, 0.0) - (-0.000347)) > eps) {
printf("Coordinate ( 0.5, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.5, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(0.9, 0.0) - (-0.000047)) > eps) {
printf("Coordinate ( 0.9, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(0.9, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(1.3, 0.0) - (-0.000004)) > eps) {
printf("Coordinate ( 1.3, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(1.3, 0.0));
success = 0;
}
if (fabs(xvel_prev_time.get_pt_value(1.7, 0.0) - (-0.000001)) > eps) {
printf("Coordinate ( 1.7, 0.0) xvel value = %lf\n", xvel_prev_time.get_pt_value(1.7, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.1, 0.0) - (-0.100000)) > eps) {
printf("Coordinate ( 0.1, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.1, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.5, 0.0) - (0.001477)) > eps) {
printf("Coordinate ( 0.5, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.5, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(0.9, 0.0) - (0.000572)) > eps) {
printf("Coordinate ( 0.9, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(0.9, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(1.3, 0.0) - (0.000296)) > eps) {
printf("Coordinate ( 1.3, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(1.3, 0.0));
success = 0;
}
if (fabs(yvel_prev_time.get_pt_value(1.7, 0.0) - (0.000169)) > eps) {
printf("Coordinate ( 1.7, 0.0) yvel value = %lf\n", yvel_prev_time.get_pt_value(1.7, 0.0));
success = 0;
}
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// load the mesh file
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// a-priori mesh refinements
mesh.refine_all_elements();
mesh.refine_towards_boundary(5, 4, false);
mesh.refine_towards_boundary(1, 4);
mesh.refine_towards_boundary(3, 4);
// initialize shapesets and the cache
H1ShapesetBeuchler h1_shapeset;
PrecalcShapeset h1_pss(&h1_shapeset);
#ifdef PRESSURE_IN_L2
L2Shapeset l2_shapeset;
PrecalcShapeset l2_pss(&l2_shapeset);
#endif
// spaces for velocities and pressure
H1Space xvel_space(&mesh, &h1_shapeset);
H1Space yvel_space(&mesh, &h1_shapeset);
#ifdef PRESSURE_IN_L2
L2Space p_space(&mesh, &l2_shapeset);
#else
H1Space p_space(&mesh, &h1_shapeset);
#endif
// initialize boundary conditions
xvel_space.set_bc_types(xvel_bc_type);
xvel_space.set_bc_values(xvel_bc_value);
yvel_space.set_bc_types(yvel_bc_type);
p_space.set_bc_types(p_bc_type);
// set velocity and pressure polynomial degrees
xvel_space.set_uniform_order(P_INIT_VEL);
yvel_space.set_uniform_order(P_INIT_VEL);
p_space.set_uniform_order(P_INIT_PRESSURE);
// assign degrees of freedom
int ndofs = 0;
ndofs += xvel_space.assign_dofs(ndofs);
ndofs += yvel_space.assign_dofs(ndofs);
ndofs += p_space.assign_dofs(ndofs);
// solutions for the Newton's iteration and time stepping
Solution xvel_prev_time, yvel_prev_time, xvel_prev_newton, yvel_prev_newton, p_prev;
xvel_prev_time.set_zero(&mesh);
yvel_prev_time.set_zero(&mesh);
xvel_prev_newton.set_zero(&mesh);
yvel_prev_newton.set_zero(&mesh);
p_prev.set_zero(&mesh);
// set up weak formulation
WeakForm wf(3);
if (NEWTON) {
wf.add_biform(0, 0, callback(bilinear_form_sym_0_0_1_1), SYM);
wf.add_biform(0, 0, callback(newton_bilinear_form_unsym_0_0), UNSYM, ANY, 2, &xvel_prev_newton, &yvel_prev_newton);
wf.add_biform(0, 1, callback(newton_bilinear_form_unsym_0_1), UNSYM, ANY, 1, &xvel_prev_newton);
wf.add_biform(0, 2, callback(bilinear_form_unsym_0_2), ANTISYM);
wf.add_biform(1, 0, callback(newton_bilinear_form_unsym_1_0), UNSYM, ANY, 1, &yvel_prev_newton);
wf.add_biform(1, 1, callback(bilinear_form_sym_0_0_1_1), SYM);
wf.add_biform(1, 1, callback(newton_bilinear_form_unsym_1_1), UNSYM, ANY, 2, &xvel_prev_newton, &yvel_prev_newton);
wf.add_biform(1, 2, callback(bilinear_form_unsym_1_2), ANTISYM);
wf.add_liform(0, callback(newton_F_0), ANY, 5, &xvel_prev_time, &yvel_prev_time, &xvel_prev_newton, &yvel_prev_newton, &p_prev);
wf.add_liform(1, callback(newton_F_1), ANY, 5, &xvel_prev_time, &yvel_prev_time, &xvel_prev_newton, &yvel_prev_newton, &p_prev);
wf.add_liform(2, callback(newton_F_2), ANY, 2, &xvel_prev_newton, &yvel_prev_newton);
}
else {
wf.add_biform(0, 0, callback(bilinear_form_sym_0_0_1_1), SYM);
wf.add_biform(0, 0, callback(simple_bilinear_form_unsym_0_0_1_1), UNSYM, ANY, 2, &xvel_prev_time, &yvel_prev_time);
wf.add_biform(1, 1, callback(bilinear_form_sym_0_0_1_1), SYM);
wf.add_biform(1, 1, callback(simple_bilinear_form_unsym_0_0_1_1), UNSYM, ANY, 2, &xvel_prev_time, &yvel_prev_time);
wf.add_biform(0, 2, callback(bilinear_form_unsym_0_2), ANTISYM);
wf.add_biform(1, 2, callback(bilinear_form_unsym_1_2), ANTISYM);
wf.add_liform(0, callback(simple_linear_form), ANY, 1, &xvel_prev_time);
wf.add_liform(1, callback(simple_linear_form), ANY, 1, &yvel_prev_time);
}
// visualization
VectorView vview("velocity [m/s]", 0, 0, 1500, 470);
ScalarView pview("pressure [Pa]", 0, 530, 1500, 470);
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);
// matrix solver
UmfpackSolver umfpack;
// linear system
LinSystem ls(&wf, &umfpack);
// nonlinear system
NonlinSystem nls(&wf, &umfpack);
if (NEWTON) {
// set up the nonlinear system
nls.set_spaces(3, &xvel_space, &yvel_space, &p_space);
#ifdef PRESSURE_IN_L2
nls.set_pss(3, &h1_pss, &h1_pss, &l2_pss);
#else
nls.set_pss(1, &h1_pss);
#endif
}
else {
// set up the linear system
ls.set_spaces(3, &xvel_space, &yvel_space, &p_space);
#ifdef PRESSURE_IN_L2
ls.set_pss(3, &h1_pss, &h1_pss, &l2_pss);
#else
ls.set_pss(1, &h1_pss);
#endif
}
// time-stepping loop
char title[100];
int num_time_steps = T_FINAL / TAU;
for (int i = 1; i <= num_time_steps; i++)
{
TIME += TAU;
info("\n---- Time step %d, time = %g:\n", i, TIME);
// this is needed to update the time-dependent boundary conditions
ndofs = 0;
ndofs += xvel_space.assign_dofs(ndofs);
ndofs += yvel_space.assign_dofs(ndofs);
ndofs += p_space.assign_dofs(ndofs);
if (NEWTON) {
// Newton's method
if (!nls.solve_newton_3(&xvel_prev_newton, &yvel_prev_newton, &p_prev, NEWTON_TOL, NEWTON_MAX_ITER)) error("Newton's method did not converge.");
// show the solution at the end of time step
sprintf(title, "Velocity, time %g", TIME);
vview.set_title(title);
vview.show(&xvel_prev_newton, &yvel_prev_newton, EPS_LOW);
sprintf(title, "Pressure, time %g", TIME);
pview.set_title(title);
pview.show(&p_prev);
// copy the result of the Newton's iteration into the
// previous time level solutions
xvel_prev_time.copy(&xvel_prev_newton);
yvel_prev_time.copy(&yvel_prev_newton);
}
else {
// assemble and solve
Solution xvel_sln, yvel_sln, p_sln;
ls.assemble();
ls.solve(3, &xvel_sln, &yvel_sln, &p_sln);
// show the solution at the end of time step
sprintf(title, "Velocity, time %g", TIME);
vview.set_title(title);
vview.show(&xvel_sln, &yvel_sln, EPS_LOW);
sprintf(title, "Pressure, time %g", TIME);
pview.set_title(title);
pview.show(&p_sln);
// this copy destroys xvel_sln and yvel_sln
// which are no longer needed
xvel_prev_time = xvel_sln;
yvel_prev_time = yvel_sln;
}
}
// wait for keyboard or mouse input
View::wait();
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;
}
