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example_5_1_2.py
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import numpy as np
import scipy.sparse as sps
from porepy.viz import exporter
from porepy.fracs import importer
from porepy.params import tensor
from porepy.params.bc import BoundaryCondition
from porepy.params.data import Parameters
from porepy.grids import coarsening as co
from porepy.numerics.vem import dual
from porepy.utils import comp_geom as cg
from porepy.utils import sort_points
# ------------------------------------------------------------------------------#
def add_data(gb, domain):
"""
Define the permeability, apertures, boundary conditions
"""
gb.add_node_props(["param", "is_tangent"])
tol = 1e-3
a = 1e-2
for g, d in gb:
param = Parameters(g)
# Permeability
d["is_tangential"] = True
if g.dim == 2:
kxx = 1e-14 * np.ones(g.num_cells)
else:
kxx = 1e-8 * np.ones(g.num_cells)
perm = tensor.SecondOrderTensor(g.dim, kxx)
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[np.logical_or(left, right)] = "dir"
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces[left]] = 1013250
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"] = 1e-10 * np.ones(gn[0].num_cells) / aperture
# ------------------------------------------------------------------------------#
def plot_over_line(gb, pts, name, tol):
values = np.zeros(pts.shape[1])
is_found = np.zeros(pts.shape[1], dtype=np.bool)
for g, d in gb:
if g.dim < gb.dim_max():
continue
if not cg.is_planar(np.hstack((g.nodes, pts)), tol=1e-4):
continue
faces_cells, _, _ = sps.find(g.cell_faces)
nodes_faces, _, _ = sps.find(g.face_nodes)
normal = cg.compute_normal(g.nodes)
for c in np.arange(g.num_cells):
loc = slice(g.cell_faces.indptr[c], g.cell_faces.indptr[c + 1])
pts_id_c = np.array(
[
nodes_faces[g.face_nodes.indptr[f] : g.face_nodes.indptr[f + 1]]
for f in faces_cells[loc]
]
).T
pts_id_c = sort_points.sort_point_pairs(pts_id_c)[0, :]
pts_c = g.nodes[:, pts_id_c]
mask = np.where(np.logical_not(is_found))[0]
if mask.size == 0:
break
check = np.zeros(mask.size, dtype=np.bool)
last = False
for i, pt in enumerate(pts[:, mask].T):
check[i] = cg.is_point_in_cell(pts_c, pt)
if last and not check[i]:
break
is_found[mask] = check
values[mask[check]] = d[name][c]
return values
##------------------------------------------------------------------------------#
tol = 1e-4
mesh_kwargs = {"mesh_size_frac": 500, "mesh_size_min": 20}
domain = {"xmin": 0, "xmax": 700, "ymin": 0, "ymax": 600}
gb = importer.from_csv("network.csv", mesh_kwargs, domain)
gb.compute_geometry()
co.coarsen(gb, "by_volume")
gb.assign_node_ordering()
# Assign parameters
add_data(gb, domain)
# Choose and define the solvers and coupler
solver = dual.DualVEMMixDim("flow")
A, b = solver.matrix_rhs(gb)
up = sps.linalg.spsolve(A, b)
solver.split(gb, "up", up)
gb.add_node_props(["discharge", "pressure", "P0u"])
solver.extract_u(gb, "up", "discharge")
solver.extract_p(gb, "up", "pressure")
solver.project_u(gb, "discharge", "P0u")
exporter.export_vtk(gb, "vem", ["pressure", "P0u"], folder="example_5_1_2")
# This part is very slow and not optimized, it's just to obtain the plots once.
b_box = gb.bounding_box()
N_pts = 1000
y_range = np.linspace(b_box[0][1] + tol, b_box[1][1] - tol, N_pts)
pts = np.stack((625 * np.ones(N_pts), y_range, np.zeros(N_pts)))
values = plot_over_line(gb, pts, "pressure", tol)
arc_length = y_range - b_box[0][1]
np.savetxt("example_5_1_2/vem_x_625.csv", (arc_length, values))
x_range = np.linspace(b_box[0][0] + tol, b_box[1][0] - tol, N_pts)
pts = np.stack((x_range, 500 * np.ones(N_pts), np.zeros(N_pts)))
values = plot_over_line(gb, pts, "pressure", tol)
arc_length = x_range - b_box[0][0]
np.savetxt("example_5_1_2/vem_y_500.csv", (arc_length, values))
print("diam", gb.diameter(lambda g: g.dim == gb.dim_max()))
print("num_cells 2d", gb.num_cells(lambda g: g.dim == 2))
print("num_cells 1d", gb.num_cells(lambda g: g.dim == 1))