def test_steady_stokes(k): # Polynomial order and mesh resolution nx_list = [4, 8, 16] nu = Constant(1) if comm.Get_rank() == 0: print('{:=^72}'.format('Computing for polynomial order ' + str(k))) # Error listst error_u, error_p, error_div = [], [], [] for nx in nx_list: if comm.Get_rank() == 0: print('# Resolution ' + str(nx)) mesh = UnitSquareMesh(nx, nx) # Get forcing from exact solutions u_exact, p_exact = exact_solution(mesh) f = div(p_exact * Identity(2) - 2 * nu * sym(grad(u_exact))) # Define FunctionSpaces and functions V = VectorElement("DG", mesh.ufl_cell(), k) Q = FiniteElement("DG", mesh.ufl_cell(), k - 1) Vbar = VectorElement("DGT", mesh.ufl_cell(), k) Qbar = FiniteElement("DGT", mesh.ufl_cell(), k) mixedL = FunctionSpace(mesh, MixedElement([V, Q])) mixedG = FunctionSpace(mesh, MixedElement([Vbar, Qbar])) Uh = Function(mixedL) Uhbar = Function(mixedG) # Set forms alpha = Constant(6 * k * k) forms_stokes = FormsStokes(mesh, mixedL, mixedG, alpha).forms_steady(nu, f) # No-slip boundary conditions, set pressure in one of the corners bc0 = DirichletBC(mixedG.sub(0), Constant((0, 0)), Gamma) bc1 = DirichletBC(mixedG.sub(1), Constant(0), Corner, "pointwise") bcs = [bc0, bc1] # Initialize static condensation class ssc = StokesStaticCondensation(mesh, forms_stokes['A_S'], forms_stokes['G_S'], forms_stokes['B_S'], forms_stokes['Q_S'], forms_stokes['S_S'], bcs) # Assemble global system and incorporates bcs ssc.assemble_global_system(True) # Solve using mumps ssc.solve_problem(Uhbar, Uh, "mumps", "default") # Compute velocity/pressure/local div error uh, ph = Uh.split() e_u = np.sqrt(np.abs(assemble(dot(uh - u_exact, uh - u_exact) * dx))) e_p = np.sqrt(np.abs(assemble((ph - p_exact) * (ph - p_exact) * dx))) e_d = np.sqrt(np.abs(assemble(div(uh) * div(uh) * dx))) if comm.rank == 0: error_u.append(e_u) error_p.append(e_p) error_div.append(e_d) print('Error in velocity ' + str(error_u[-1])) print('Error in pressure ' + str(error_p[-1])) print('Local mass error ' + str(error_div[-1])) if comm.rank == 0: iterator_list = [1. / float(nx) for nx in nx_list] conv_u = compute_convergence(iterator_list, error_u) conv_p = compute_convergence(iterator_list, error_p) assert any(conv > k + 0.75 for conv in conv_u) assert any(conv > (k - 1) + 0.75 for conv in conv_p)
with open(fname, "a" if append else "w") as fi: fi.write(",".join(map(lambda v: "%.6e" % v, vals)) + "\n") # Compute and output functionals def output_data_step(append=False): urms = (1.0 / (lmbdax*lmbdaz) * assemble(dot(u_vec, u_vec) * dx)) ** 0.5 conservation = abs(assemble(phi * dx) - conservation0) entrainment = assemble(1.0 / (lmbdax * lmbdaz * Constant(db)) * phi * dx(de)) output_functionals(data_filename, [float(t), float(dt), urms, conservation, entrainment], append=append) # Initial Stokes solve time = Timer("ZZZ Stokes assemble") ssc.assemble_global_system(True) del time time = Timer("ZZZ Stokes solve") for bc in bcs: ssc.apply_boundary(bc) ssc.solve_problem(Uhbar.cpp_object(), Uh.cpp_object(), "mumps", "default") del time # Transfer the computed velocity function and compute functionals velocity_assigner.assign(u_vec, Uh.sub(0)) output_data_step(append=False) time_snap_shot_interval = 5.0 next_snap_shot_time = time_snap_shot_interval for j in range(50000):