def test_upwind_coupling_3d_2d_left_right(self):
f = np.array([[ 0, 1, 1, 0],
[ 0, 0, 1, 1],
[.5, .5, .5, .5]])
gb = meshing.cart_grid( [f], [1, 1, 2], **{'physdims': [1, 1, 1]})
gb.compute_geometry()
gb.assign_node_ordering()
tol = 1e-3
solver = upwind.UpwindMixedDim('transport')
gb.add_node_props(['param'])
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells)*np.power(1e-2, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [1, 0, 0], aperture)
bound_faces = g.get_boundary_faces()
bound_face_centers = g.face_centers[:, bound_faces]
left = bound_face_centers[0, :] < tol
right = bound_face_centers[0, :] > 1 - tol
labels = np.array(['neu'] * bound_faces.size)
labels[np.logical_or(left, right)] = ['dir']
bc_val = np.zeros(g.num_faces)
bc_dir = bound_faces[np.logical_or(left, right)]
bc_val[bc_dir] = 1
param.set_bc('transport', BoundaryCondition(g, bound_faces, labels))
param.set_bc_val('transport', bc_val)
d['param'] = param
# Assign coupling discharge
gb.add_edge_prop('param')
for e, d in gb.edges_props():
g_h = gb.sorted_nodes_of_edge(e)[1]
discharge = gb.node_prop(g_h,'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
U, rhs = solver.matrix_rhs(gb)
deltaT = solver.cfl(gb)
U_known = np.array([[.5, 0, 0],
[0, .5, 0],
[0, 0, 1e-2]])
rhs_known = np.array([.5, .5, 1e-2])
deltaT_known = 5*1e-1
rtol = 1e-15
atol = rtol
assert np.allclose(U.todense(), U_known, rtol, atol)
assert np.allclose(rhs, rhs_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
def test_upwind_2d_full_beta_bc_dir(self):
f = np.array([[2, 2], [0, 2]])
gb = meshing.cart_grid([f], [4, 2])
gb.assign_node_ordering()
gb.compute_geometry()
solver = upwind.UpwindMixedDim('transport')
gb.add_node_props(['param'])
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells) * \
np.power(1e-1, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [1, 1, 0], aperture)
bound_faces = g.tags['domain_boundary_faces'].nonzero()[0]
labels = np.array(['dir'] * bound_faces.size)
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces] = 3
param.set_bc('transport', BoundaryCondition(
g, bound_faces, labels))
param.set_bc_val('transport', bc_val)
d['param'] = param
# Assign coupling discharge
gb.add_edge_props('param')
for e, d in gb.edges():
g_h = gb.nodes_of_edge(e)[1]
discharge = gb.node_props(g_h, 'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
M, rhs = solver.matrix_rhs(gb)
M_known = np.array([[2, 0, 0, 0, 0, 0, 0, 0, 0, 0.],
[-1, 2, 0, 0, 0, 0, 0, 0, 0, 0.],
[0, 0, 2, 0, 0, 0, 0, 0, 0, -1.],
[0, 0, -1, 2, 0, 0, 0, 0, 0, 0.],
[-1, 0, 0, 0, 2, 0, 0, 0, 0, 0.],
[0, -1, 0, 0, -1, 2, 0, 0, 0, 0.],
[0, 0, -1, 0, 0, 0, 2, 0, -1, 0.],
[0, 0, 0, -1, 0, 0, -1, 2, 0, 0.],
[0, 0, 0, 0, 0, -1, 0, 0, 1.1, -0.1],
[0, -1, 0, 0, 0, 0, 0, 0, 0, 1.1]])
rhs_known = np.array([6, 3, 3, 3, 3, 0, 0, 0, 0, 0.3])
rtol = 1e-15
atol = rtol
assert np.allclose(M.todense(), M_known, rtol, atol)
assert np.allclose(rhs, rhs_known, rtol, atol)
def test_upwind_2d_beta_positive(self):
f = np.array([[2, 2],
[0, 2]])
gb = meshing.cart_grid([f], [4, 2])
gb.assign_node_ordering()
gb.compute_geometry()
solver = upwind.UpwindMixedDim('transport')
gb.add_node_props(['param'])
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells) * \
np.power(1e-2, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [2, 0, 0], aperture)
bf = g.tags['domain_boundary_faces'].nonzero()[0]
bc = BoundaryCondition(g, bf, bf.size * ['neu'])
param.set_bc('transport', bc)
d['param'] = param
# Assign coupling discharge
gb.add_edge_props('param')
for e, d in gb.edges():
g_h = gb.nodes_of_edge(e)[1]
discharge = gb.node_props(g_h, 'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
M = solver.matrix_rhs(gb)[0].todense()
M_known = np.array([[2, 0, 0, 0, 0, 0, 0, 0, 0, 0.],
[-2, 2, 0, 0, 0, 0, 0, 0, 0, 0.],
[0, 0, 2, 0, 0, 0, 0, 0, 0, -2.],
[0, 0, -2, 0, 0, 0, 0, 0, 0, 0.],
[0, 0, 0, 0, 2, 0, 0, 0, 0, 0.],
[0, 0, 0, 0, -2, 2, 0, 0, 0, 0.],
[0, 0, 0, 0, 0, 0, 2, 0, -2, 0.],
[0, 0, 0, 0, 0, 0, -2, 0, 0, 0.],
[0, 0, 0, 0, 0, -2, 0, 0, 2, 0.],
[0, -2, 0, 0, 0, 0, 0, 0, 0, 2.]])
rtol = 1e-15
atol = rtol
assert np.allclose(M, M_known, rtol, atol)
total_flow_rate = 0
for g, d in gb:
bound_faces = g.tags['domain_boundary_faces'].nonzero()[0]
if bound_faces.size != 0:
bound_face_centers = g.face_centers[:, bound_faces]
left = bound_face_centers[0, :] < domain['xmin'] + tol
flow_rate = d['u'][bound_faces[left]]
total_flow_rate += np.sum(flow_rate)
print("total flow rate", total_flow_rate)
exporter.export_vtk(gb, 'darcy', ['pressure', "P0u"], folder=export_folder)
#################################################################
physics = 'transport'
advection = upwind.UpwindMixedDim(physics)
diffusion = tpfa.TpfaMixedDim(physics)
mass = mass_matrix.MassMatrixMixedDim(physics)
invMass = mass_matrix.InvMassMatrixMixedDim(physics)
# Assign parameters
add_data_advection_diffusion(gb, domain, tol, a)
T = 1
deltaT = 0.01
gb.add_node_prop('deltaT', prop=deltaT)
U, rhs_u = advection.matrix_rhs(gb)
D, rhs_d = diffusion.matrix_rhs(gb)
M, _ = mass.matrix_rhs(gb)
OF = advection.outflow(gb)
def test_upwind_coupling_3d_2d_1d_0d(self):
f1 = np.array([[ 0, 1, 1, 0],
[ 0, 0, 1, 1],
[.5, .5, .5, .5]])
f2 = np.array([[.5, .5, .5, .5],
[ 0, 1, 1, 0],
[ 0, 0, 1, 1]])
f3 = np.array([[ 0, 1, 1, 0],
[.5, .5, .5, .5],
[ 0, 0, 1, 1]])
gb = meshing.cart_grid([f1, f2, f3], [2, 2, 2],
**{'physdims': [1, 1, 1]})
gb.compute_geometry()
gb.assign_node_ordering()
cell_centers1 = np.array([[ 0.25 , 0.75 , 0.25 , 0.75],
[ 0.25 , 0.25 , 0.75 , 0.75],
[ 0.5 , 0.5 , 0.5 , 0.5 ]])
cell_centers2 = np.array([[ 0.5 , 0.5 , 0.5 , 0.5 ],
[ 0.25 , 0.25 , 0.75 , 0.75],
[ 0.75 , 0.25 , 0.75 , 0.25]])
cell_centers3 = np.array([[ 0.25 , 0.75 , 0.25 , 0.75],
[ 0.5 , 0.5 , 0.5 , 0.5 ],
[ 0.25 , 0.25 , 0.75 , 0.75]])
cell_centers4 = np.array([[ 0.5 ], [ 0.25], [ 0.5 ]])
cell_centers5 = np.array([[ 0.5 ], [ 0.75], [ 0.5 ]])
cell_centers6 = np.array([[ 0.75], [ 0.5 ], [ 0.5 ]])
cell_centers7 = np.array([[ 0.25], [ 0.5 ], [ 0.5 ]])
cell_centers8 = np.array([[ 0.5 ], [ 0.5 ], [ 0.25]])
cell_centers9 = np.array([[ 0.5 ], [ 0.5 ], [ 0.75]])
for g, d in gb:
if np.allclose(g.cell_centers[:, 0], cell_centers1[:, 0]):
d['node_number'] = 1
elif np.allclose(g.cell_centers[:, 0], cell_centers2[:, 0]):
d['node_number'] = 2
elif np.allclose(g.cell_centers[:, 0], cell_centers3[:, 0]):
d['node_number'] = 3
elif np.allclose(g.cell_centers[:, 0], cell_centers4[:, 0]):
d['node_number'] = 4
elif np.allclose(g.cell_centers[:, 0], cell_centers5[:, 0]):
d['node_number'] = 5
elif np.allclose(g.cell_centers[:, 0], cell_centers6[:, 0]):
d['node_number'] = 6
elif np.allclose(g.cell_centers[:, 0], cell_centers7[:, 0]):
d['node_number'] = 7
elif np.allclose(g.cell_centers[:, 0], cell_centers8[:, 0]):
d['node_number'] = 8
elif np.allclose(g.cell_centers[:, 0], cell_centers9[:, 0]):
d['node_number'] = 9
else:
pass
tol = 1e-3
solver = upwind.UpwindMixedDim('transport')
gb.add_node_props(['param'])
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells)*np.power(1e-2, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [1, 0, 0], aperture)
bound_faces = g.get_boundary_faces()
bound_face_centers = g.face_centers[:, bound_faces]
left = bound_face_centers[0, :] < tol
right = bound_face_centers[0, :] > 1 - tol
labels = np.array(['neu'] * bound_faces.size)
labels[np.logical_or(left, right)] = ['dir']
bc_val = np.zeros(g.num_faces)
bc_dir = bound_faces[np.logical_or(left, right)]
bc_val[bc_dir] = 1
param.set_bc('transport', BoundaryCondition(g, bound_faces, labels))
param.set_bc_val('transport', bc_val)
d['param'] = param
# Assign coupling discharge
gb.add_edge_prop('param')
for e, d in gb.edges_props():
g_h = gb.sorted_nodes_of_edge(e)[1]
discharge = gb.node_prop(g_h,'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
U, rhs = solver.matrix_rhs(gb)
deltaT = solver.cfl(gb)
U_known, rhs_known = matrix_rhs_for_test_upwind_coupling_3d_2d_1d_0d()
deltaT_known = 5*1e-3
rtol = 1e-15
atol = rtol
assert np.allclose(U.todense(), U_known, rtol, atol)
assert np.allclose(rhs, rhs_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
def test_upwind_coupling_2d_1d_left_right_cross(self):
f1 = np.array([[0, 2],
[1, 1]])
f2 = np.array([[1, 1],
[0, 2]])
gb = meshing.cart_grid( [f1, f2], [2, 2])
gb.compute_geometry()
gb.assign_node_ordering()
# Enforce node orderning because of Python 3.5 and 2.7.
# Don't do it in general.
cell_centers_1 = np.array([[ 1.50000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00],
[ -5.55111512e-17, 5.55111512e-17]])
cell_centers_2 = np.array([[ 1.00000000e+00, 1.00000000e+00],
[ 1.50000000e+00, 5.00000000e-01],
[ -5.55111512e-17, 5.55111512e-17]])
for g, d in gb:
if g.dim == 1:
if np.allclose(g.cell_centers, cell_centers_1):
d['node_number'] = 1
elif np.allclose(g.cell_centers, cell_centers_2):
d['node_number'] = 2
else:
raise ValueError('Grid not found')
tol = 1e-3
solver = upwind.UpwindMixedDim('transport')
gb.add_node_props(['param'])
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells)*np.power(1e-2, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [1, 0, 0], aperture)
bound_faces = g.get_boundary_faces()
bound_face_centers = g.face_centers[:, bound_faces]
left = bound_face_centers[0, :] < tol
right = bound_face_centers[0, :] > 2 - tol
labels = np.array(['neu'] * bound_faces.size)
labels[np.logical_or(left, right)] = ['dir']
bc_val = np.zeros(g.num_faces)
bc_dir = bound_faces[np.logical_or(left, right)]
bc_val[bc_dir] = 1
param.set_bc('transport', BoundaryCondition(g, bound_faces, labels))
param.set_bc_val('transport', bc_val)
d['param'] = param
# Assign coupling discharge
gb.add_edge_prop('param')
for e, d in gb.edges_props():
g_h = gb.sorted_nodes_of_edge(e)[1]
discharge = gb.node_prop(g_h,'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
U, rhs = solver.matrix_rhs(gb)
deltaT = solver.cfl(gb)
U_known = np.array(\
[[ 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[ 0. , 1. , 0. , 0. , 0. , 0. , 0. , -1. , 0. ],
[ 0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 1. , 0. , 0. , -1. , 0. , 0. ],
[ 0. , 0. , 0. , 0. , 0.01, 0. , 0. , 0. , -0.01],
[ 0. , 0. , 0. , 0. , 0. , 0.01, 0. , 0. , 0. ],
[ 0. , 0. , -1. , 0. , 0. , 0. , 1. , 0. , 0. ],
[-1. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. ],
[ 0. , 0. , 0. , 0. , 0. , -0.01, 0. , 0. , 0.01]])
rhs_known = np.array([ 1., 0., 1., 0., 0., 0.01, 0., 0., 0.])
deltaT_known = 5*1e-3
rtol = 1e-15
atol = rtol
assert np.allclose(U.todense(), U_known, rtol, atol)
assert np.allclose(rhs, rhs_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
def test_upwind_coupling_2d_1d_bottom_top(self):
f = np.array([[0, 1],
[1, 1]])
gb = meshing.cart_grid([f], [1, 2])
gb.compute_geometry()
gb.assign_node_ordering()
tol = 1e-3
gb.add_node_props(['param'])
solver = upwind.UpwindMixedDim('transport')
for g, d in gb:
param = Parameters(g)
aperture = np.ones(g.num_cells) * \
np.power(1e-2, gb.dim_max() - g.dim)
param.set_aperture(aperture)
d['discharge'] = solver.discr.discharge(g, [0, 1, 0], aperture)
bound_faces = g.tags['domain_boundary_faces'].nonzero()[0]
if bound_faces.size != 0:
bound_face_centers = g.face_centers[:, bound_faces]
top = bound_face_centers[1, :] > 2 - tol
bottom = bound_face_centers[1, :] < tol
labels = np.array(['neu'] * bound_faces.size)
labels[np.logical_or(top, bottom)] = ['dir']
bc_val = np.zeros(g.num_faces)
bc_dir = bound_faces[np.logical_or(top, bottom)]
bc_val[bc_dir] = 1
param.set_bc('transport', BoundaryCondition(
g, bound_faces, labels))
param.set_bc_val('transport', bc_val)
d['param'] = param
# Assign coupling discharge
gb.add_edge_props('param')
for e, d in gb.edges():
g_h = gb.nodes_of_edge(e)[1]
discharge = gb.node_props(g_h, 'discharge')
d['param'] = Parameters(g_h)
d['discharge'] = discharge
U, rhs = solver.matrix_rhs(gb)
deltaT = solver.cfl(gb)
U_known = np.array([[1, 0, 0],
[0, 1, -1],
[-1, 0, 1]])
rhs_known = np.array([1, 0, 0])
deltaT_known = 5 * 1e-3
rtol = 1e-15
atol = rtol
assert np.allclose(U.todense(), U_known, rtol, atol)
assert np.allclose(rhs, rhs_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
