def add_data(gb, domain, kf):
"""
Define the permeability, apertures, boundary conditions
"""
gb.add_node_props(['param'])
tol = 1e-5
a = 1e-4
for g, d in gb:
param = Parameters(g)
# Permeability
kxx = np.ones(g.num_cells) * np.power(kf, g.dim < gb.dim_max())
if g.dim == 2:
perm = tensor.SecondOrderTensor(3, kxx=kxx, kyy=kxx, kzz=1)
else:
perm = tensor.SecondOrderTensor(3, kxx=kxx, kyy=1, kzz=1)
if g.dim == 1:
R = cg.project_line_matrix(g.nodes, reference=[1, 0, 0])
perm.rotate(R)
param.set_tensor("flow", perm)
# Source term
param.set_source("flow", np.zeros(g.num_cells))
# Assign apertures
aperture = np.power(a, gb.dim_max() - g.dim)
param.set_aperture(np.ones(g.num_cells) * aperture)
# Boundaries
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
right = bound_face_centers[0, :] > domain['xmax'] - tol
labels = np.array(['neu'] * bound_faces.size)
labels[right] = 'dir'
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces[left]] = -aperture \
* g.face_areas[bound_faces[left]]
bc_val[bound_faces[right]] = 1
param.set_bc("flow", BoundaryCondition(g, bound_faces, labels))
param.set_bc_val("flow", bc_val)
else:
param.set_bc("flow", BoundaryCondition(g, np.empty(0),
np.empty(0)))
d['param'] = param
# Assign coupling permeability
gb.add_edge_prop('kn')
for e, d in gb.edges_props():
gn = gb.sorted_nodes_of_edge(e)
aperture = np.power(a, gb.dim_max() - gn[0].dim)
d['kn'] = np.ones(gn[0].num_cells) * kf / aperture
def create_embedded_line_grid(loc_coord, glob_id, tol=1e-4):
loc_center = np.mean(loc_coord, axis=1).reshape((-1, 1))
loc_coord -= loc_center
# Check that the points indeed form a line
if not cg.is_collinear(loc_coord, tol):
raise ValueError("Elements are not colinear")
# Find the tangent of the line
tangent = cg.compute_tangent(loc_coord)
# Projection matrix
rot = cg.project_line_matrix(loc_coord, tangent)
loc_coord_1d = rot.dot(loc_coord)
# The points are now 1d along one of the coordinate axis, but we
# don't know which yet. Find this.
sum_coord = np.sum(np.abs(loc_coord_1d), axis=1)
sum_coord /= np.amax(sum_coord)
active_dimension = np.logical_not(
np.isclose(sum_coord, 0, atol=tol, rtol=0))
# Check that we are indeed in 1d
assert np.sum(active_dimension) == 1
# Sort nodes, and create grid
coord_1d = loc_coord_1d[active_dimension]
sort_ind = np.argsort(coord_1d)[0]
sorted_coord = coord_1d[0, sort_ind]
g = structured.TensorGrid(sorted_coord)
# Project back to active dimension
nodes = np.zeros(g.nodes.shape)
nodes[active_dimension] = g.nodes[0]
g.nodes = nodes
# Project back again to 3d coordinates
irot = rot.transpose()
g.nodes = irot.dot(g.nodes)
g.nodes += loc_center
# Add mapping to global point numbers
g.global_point_ind = glob_id[sort_ind]
return g
def add_data(gb, domain, kf):
"""
Define the permeability, apertures, boundary conditions
"""
gb.add_node_props(['param'])
tol = 1e-5
a = 1e-3
for g, d in gb:
param = Parameters(g)
# Permeability
kxx = np.ones(g.num_cells) * np.power(kf, g.dim < gb.dim_max())
if g.dim == 2:
perm = tensor.SecondOrderTensor(3, kxx=kxx, kyy=kxx, kzz=1)
else:
perm = tensor.SecondOrderTensor(3, kxx=kxx, kyy=1, kzz=1)
if g.dim == 1:
R = cg.project_line_matrix(g.nodes, reference=[1, 0, 0])
perm.rotate(R)
param.set_tensor("flow", perm)
# Source term
param.set_source("flow", np.zeros(g.num_cells))
# Assign apertures
aperture = np.power(a, gb.dim_max() - g.dim)
param.set_aperture(np.ones(g.num_cells) * aperture)
# Boundaries
bound_faces = g.tags['domain_boundary_faces'].nonzero()[0]
if bound_faces.size != 0:
bound_face_centers = g.face_centers[:, bound_faces]
bottom_corner = np.logical_and(bound_face_centers[0, :] < 0.1,
bound_face_centers[1, :] < 0.1)
top_corner = np.logical_and(bound_face_centers[0, :] > 0.9,
bound_face_centers[1, :] > 0.9)
labels = np.array(['neu'] * bound_faces.size)
dir_faces = np.logical_or(bottom_corner, top_corner)
labels[dir_faces] = 'dir'
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces[bottom_corner]] = 1
bc_val[bound_faces[top_corner]] = -1
param.set_bc("flow", BoundaryCondition(g, bound_faces, labels))
param.set_bc_val("flow", bc_val)
else:
param.set_bc("flow", BoundaryCondition(g, np.empty(0),
np.empty(0)))
d['param'] = param
# Assign coupling permeability
gb.add_edge_prop('kn')
for e, d in gb.edges_props():
g = gb.sorted_nodes_of_edge(e)[0]
d['kn'] = kf / gb.node_prop(g, 'param').get_aperture()