def flux_disc(self): if self.mp: return mpfa.MpfaMixedDim(physics=self.physics) elif self.mix: return MixedDiscretization(self.physics) else: return tpfa.TpfaMixedDim(physics=self.physics)
def test_mpfa_matching_grids_refine_1d_no_flow(self): gb = self.set_grids(N=[1, 2], num_nodes_mortar=2, num_nodes_1d=3) self.set_param_flow(gb, no_flow=True) solver_flow = mpfa.MpfaMixedDim("flow") A_flow, b_flow = solver_flow.matrix_rhs(gb) p = sps.linalg.spsolve(A_flow, b_flow) self.assertTrue(np.all(p[:4] == 1)) self.assertTrue(np.all(p[4:] == 0))
def test_mpfa_matching_grids_refine_mortar_no_flow(self): gb = self.set_grids(N=[1, 2], num_nodes_mortar=3, num_nodes_1d=2) self.set_param_flow(gb, no_flow=True) solver_flow = mpfa.MpfaMixedDim("flow") A_flow, b_flow = solver_flow.matrix_rhs(gb) for e, d in gb.edges(): mg = d["mortar_grid"] p = sps.linalg.spsolve(A_flow, b_flow) self.assertTrue(np.all(p[:3] == 1)) self.assertTrue(np.all(p[3:] == 0))
def test_mpfa_matching_grids_refine_2d_uniform_flow(self): kn = 1e4 gb = self.set_grids(N=[2, 2], num_nodes_mortar=2, num_nodes_1d=2) self.set_param_flow(gb, no_flow=False, kn=kn) solver_flow = mpfa.MpfaMixedDim("flow") A_flow, b_flow = solver_flow.matrix_rhs(gb) p = sps.linalg.spsolve(A_flow, b_flow) solver_flow.split(gb, "pressure", p) g_2d = gb.grids_of_dimension(2)[0] p_2d = gb.node_props(g_2d, "pressure") # NOTE: This will not be entirely correct due to impact of normal permeability at fracture self.assertTrue(np.allclose(p_2d, g_2d.cell_centers[1], rtol=1e-4)) g_1d = gb.grids_of_dimension(1)[0] p_1d = gb.node_props(g_1d, "pressure") # NOTE: This will not be entirely correct, self.assertTrue(np.allclose(p_1d, g_1d.cell_centers[1]))
def main(kf, description, multi_point, if_export=False): # Define the geometry and produce the meshes mesh_kwargs = {} mesh_size = 0.045 mesh_kwargs['mesh_size'] = { 'mode': 'constant', 'value': mesh_size, 'bound_value': mesh_size } domain = {'xmin': 0, 'xmax': 1, 'ymin': 0, 'ymax': 1} file_name = 'network_geiger.csv' write_network(file_name) gb = importer.dfm_2d_from_csv(file_name, mesh_kwargs, domain) gb.compute_geometry() gb.assign_node_ordering() # Assign parameters add_data(gb, domain, kf, mesh_size) # Choose discretization and define the solver if multi_point: solver = mpfa.MpfaMixedDim('flow') else: solver = tpfa.TpfaMixedDim('flow') # Discretize A, b = solver.matrix_rhs(gb) # Solve the linear system p = sps.linalg.spsolve(A, b) # Store the solution gb.add_node_props(['pressure']) solver.split(gb, 'pressure', p) if if_export: save = Exporter(gb, "fv", folder="fv_" + description) save.write_vtk(['pressure'])
def flux_disc(self): return mpfa.MpfaMixedDim(physics=self.physics)
def flux_disc(self): if self.multi_point: return mpfa.MpfaMixedDim(physics=self.physics) else: return tpfa.TpfaMixedDim(physics=self.physics)
f_set = [f_1, f_2] domain = { 'xmin': -1, 'xmax': 1, 'ymin': -1, 'ymax': 1 } # , 'zmin': -1, 'zmax': 1} gb = meshing.simplex_grid(f_set, domain) gb.assign_node_ordering() # Assign parameters add_data(gb) # Choose and define the solvers and coupler solver = mpfa.MpfaMixedDim() A, b = solver.matrix_rhs(gb) p = sps.linalg.spsolve(A.copy(), b) # Solve the problem without 0d grids. eliminate_dim = 0 p_full_condensation, p_reduced, _, _ = condensation.solve_static_condensation( A, b, gb, eliminate_dim) # The p_reduced only has pressures for the cells of grids of dim>0, so # should be plotted on a grid where the 0d has been removed: gb_r, _ = gb.duplicate_without_dimension(0) # Add the solutions to data fields in the grid buckets gb.add_node_props(['pressure', "p_condensation"]) gb_r.add_node_props(["p_reduced"])
def run_mpfa(self, gb): solver_flow = mpfa.MpfaMixedDim("flow") A_flow, b_flow = solver_flow.matrix_rhs(gb) p = sps.linalg.spsolve(A_flow, b_flow) solver_flow.split(gb, "pressure", p)
def test_mpfa_fluxes_2d_1d_left_right_dir_neu(self): """ Grid: 2 x 2 cells in matrix + 2 cells in the fracture from left to right. Dirichlet + inflow + no-flow, conductive fracture. Tests pressure solution and fluxes. """ f = np.array([[0, 1], [.5, .5]]) gb = meshing.cart_grid([f], [2, 2], **{'physdims': [1, 1]}) gb.compute_geometry() gb.assign_node_ordering() tol = 1e-3 solver = mpfa.MpfaMixedDim(physics='flow') gb.add_node_props(['param']) a = 1e-2 for g, d in gb: param = Parameters(g) a_dim = np.power(a, gb.dim_max() - g.dim) aperture = np.ones(g.num_cells) * a_dim param.set_aperture(aperture) p = tensor.SecondOrder( 3, np.ones(g.num_cells) * np.power(1e-3, g.dim < gb.dim_max())) param.set_tensor('flow', p) bound_faces = g.get_boundary_faces() bound_face_centers = g.face_centers[:, bound_faces] right = bound_face_centers[0, :] > 1 - tol left = bound_face_centers[0, :] < tol labels = np.array(['neu'] * bound_faces.size) labels[right] = ['dir'] bc_val = np.zeros(g.num_faces) bc_dir = bound_faces[right] bc_neu = bound_faces[left] bc_val[bc_dir] = g.face_centers[0, bc_dir] bc_val[bc_neu] = -g.face_areas[bc_neu] * a_dim param.set_bc('flow', bc.BoundaryCondition(g, bound_faces, labels)) param.set_bc_val('flow', bc_val) d['param'] = param gb.add_edge_prop('param') for e, d in gb.edges_props(): g_h = gb.sorted_nodes_of_edge(e)[1] d['param'] = Parameters(g_h) A, rhs = solver.matrix_rhs(gb) p = sps.linalg.spsolve(A, rhs) solver.solver.split(gb, "pressure", p) fvutils.compute_discharges(gb) p_known = np.array([ 1.7574919, 1.25249747, 1.7574919, 1.25249747, 1.25250298, 1.80993337 ]) # Known discharges d_0, d_1 = fluxes_2d_1d_left_right_dir_neu() rtol = 1e-6 atol = rtol for _, d in gb: if d['node_number'] == 0: assert np.allclose(d['discharge'], d_0, rtol, atol) if d['node_number'] == 1: assert np.allclose(d['discharge'], d_1, rtol, atol) assert np.allclose(p, p_known, rtol, atol)