/*
* Define a particular test.
*/
void TestSchnackenbergSystemOnButterflyMesh() throw (Exception)
{
/* As usual, we first create a mesh. Here we are using a 2d mesh of a butterfly-shaped domain. */
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/butterfly");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
/* We scale the mesh to an appropriate size. */
mesh.Scale(0.2, 0.2);
/* Next, we instantiate the PDE system to be solved. We pass the parameter values into the
* constructor. (The order is D,,1,, D,,2,, k,,1,, k,,-1,, k,,2,, k,,3,,) */
SchnackenbergCoupledPdeSystem<2> pde(1e-4, 1e-2, 0.1, 0.2, 0.3, 0.1);
/*
* Then we have to define the boundary conditions. As we are in 2d, {{{SPACE_DIM}}}=2 and
* {{{ELEMENT_DIM}}}=2. We also have two unknowns u and v,
* so in this case {{{PROBLEM_DIM}}}=2. The value of each boundary condition is
* given by the spatially uniform steady state solution of the Schnackenberg system,
* given by u = (k,,1,, + k,,2,,)/k,,-1,,, v = k,,2,,k,,-1,,^2^/k,,3,,(k,,1,, + k,,2,,)^2^.
*/
BoundaryConditionsContainer<2,2,2> bcc;
ConstBoundaryCondition<2>* p_bc_for_u = new ConstBoundaryCondition<2>(2.0);
ConstBoundaryCondition<2>* p_bc_for_v = new ConstBoundaryCondition<2>(0.75);
for (TetrahedralMesh<2,2>::BoundaryNodeIterator node_iter = mesh.GetBoundaryNodeIteratorBegin();
node_iter != mesh.GetBoundaryNodeIteratorEnd();
++node_iter)
{
bcc.AddDirichletBoundaryCondition(*node_iter, p_bc_for_u, 0);
bcc.AddDirichletBoundaryCondition(*node_iter, p_bc_for_v, 1);
}
/* This is the solver for solving coupled systems of linear parabolic PDEs and ODEs,
* which takes in the mesh, the PDE system, the boundary conditions and optionally
* a vector of ODE systems (one for each node in the mesh). Since in this example
* we are solving a system of coupled PDEs only, we do not supply this last argument. */
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<2,2,2> solver(&mesh, &pde, &bcc);
/* Then we set the end time and time step and the output directory to which results will be written. */
double t_end = 10;
solver.SetTimes(0, t_end);
solver.SetTimeStep(1e-1);
solver.SetSamplingTimeStep(1);
solver.SetOutputDirectory("TestSchnackenbergSystemOnButterflyMesh");
/* We create a vector of initial conditions for u and v that are random perturbations
* of the spatially uniform steady state and pass this to the solver. */
std::vector<double> init_conds(2*mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
init_conds[2*i] = fabs(2.0 + RandomNumberGenerator::Instance()->ranf());
init_conds[2*i + 1] = fabs(0.75 + RandomNumberGenerator::Instance()->ranf());
}
Vec initial_condition = PetscTools::CreateVec(init_conds);
solver.SetInitialCondition(initial_condition);
/* We now solve the PDE system and write results to VTK files, for
* visualization using Paraview. Results will be written to CHASTE_TEST_OUTPUT/TestSchnackenbergSystemOnButterflyMesh
* as a results.pvd file and several results_[time].vtu files.
* You should see something like [[Image(u.png, 350px)]] for u and [[Image(v.png, 350px)]] for v.
*/
solver.SolveAndWriteResultsToFile();
/*
* All PETSc {{{Vec}}}s should be destroyed when they are no longer needed.
*/
PetscTools::Destroy(initial_condition);
}
/**
* This test provides an example of how to solve a coupled PDE system
* where there is no coupled ODE system, and can be used as a template
* for solving standard reaction-diffusion problems arising in the
* study of pattern formation on fixed domains.
*/
void TestSchnackenbergCoupledPdeSystemIn1dWithNonZeroDirichlet()
{
// Create mesh of domain [0,1]
TrianglesMeshReader<1,1> mesh_reader("mesh/test/data/1D_0_to_1_1000_elements");
TetrahedralMesh<1,1> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Create PDE system object
SchnackenbergCoupledPdeSystem<1> pde(1e-4, 1e-2, 0.1, 0.2, 0.3, 0.1);
// Create non-zero Dirichlet boundary conditions for each state variable
BoundaryConditionsContainer<1,1,2> bcc;
ConstBoundaryCondition<1>* p_bc_for_u = new ConstBoundaryCondition<1>(2.0);
ConstBoundaryCondition<1>* p_bc_for_v = new ConstBoundaryCondition<1>(0.75);
bcc.AddDirichletBoundaryCondition(mesh.GetNode(0), p_bc_for_u, 0);
bcc.AddDirichletBoundaryCondition(mesh.GetNode(0), p_bc_for_v, 1);
bcc.AddDirichletBoundaryCondition(mesh.GetNode(mesh.GetNumNodes()-1), p_bc_for_u, 0);
bcc.AddDirichletBoundaryCondition(mesh.GetNode(mesh.GetNumNodes()-1), p_bc_for_v, 1);
// Create PDE system solver
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<1,1,2> solver(&mesh, &pde, &bcc);
// Set end time and time step
double t_end = 10;
solver.SetTimes(0, t_end);
solver.SetTimeStep(1e-1);
// Create initial conditions that are random perturbations of the uniform steady state
std::vector<double> init_conds(2*mesh.GetNumNodes());
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
init_conds[2*i] = fabs(2.0 + RandomNumberGenerator::Instance()->ranf());
init_conds[2*i + 1] = fabs(0.75 + RandomNumberGenerator::Instance()->ranf());
}
Vec initial_condition = PetscTools::CreateVec(init_conds);
solver.SetInitialCondition(initial_condition);
// Solve PDE system and store result
Vec solution = solver.Solve();
ReplicatableVector solution_repl(solution);
// Write results for visualization in gnuplot
OutputFileHandler handler("TestSchnackenbergCoupledPdeSystemIn1dWithNonZeroDirichlet", false);
out_stream results_file = handler.OpenOutputFile("schnackenberg.dat");
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double x = mesh.GetNode(i)->rGetLocation()[0];
double u = solution_repl[2*i];
double v = solution_repl[2*i + 1];
(*results_file) << x << "\t" << u << "\t" << v << "\n" << std::flush;
}
results_file->close();
std::string results_filename = handler.GetOutputDirectoryFullPath() + "schnackenberg.dat";
NumericFileComparison comp_results(results_filename, "pde/test/data/schnackenberg.dat");
TS_ASSERT(comp_results.CompareFiles(1e-3));
// Tidy up
PetscTools::Destroy(initial_condition);
PetscTools::Destroy(solution);
}
