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example_1_data.py
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example_1_data.py
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import numpy as np
from porepy.params import tensor
from porepy.params.bc import BoundaryCondition
from porepy.params.data import Parameters
# ------------------------------------------------------------------------------#
def add_data(gb, tol):
"""
Define the permeability, apertures, boundary conditions
"""
gb.add_node_props(["param"])
# Aavatsmark_transmissibilities only for tpfa intra-dimensional coupling
for g, d in gb:
d["Aavatsmark_transmissibilities"] = True
if g.dim < 2:
continue
param = Parameters(g)
# Permeability
kxx = np.array([perm(*pt) for pt in g.cell_centers.T])
param.set_tensor("flow", tensor.SecondOrderTensor(3, kxx))
# Source term
frac_id = d["frac_id"][0]
source = np.array([source_f[frac_id](*pt) for pt in g.cell_centers.T])
param.set_source("flow", g.cell_volumes * source)
# Boundaries
bound_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if bound_faces.size != 0:
bound_face_centers = g.face_centers[:, bound_faces]
labels = np.array(["dir"] * bound_faces.size)
bc_val = np.zeros(g.num_faces)
bc = [sol_f[frac_id](*pt) for pt in bound_face_centers.T]
bc_val[bound_faces] = np.array(bc)
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
gb.add_edge_prop("Aavatsmark_transmissibilities")
for _, d in gb.edges_props():
d["Aavatsmark_transmissibilities"] = True
# ------------------------------------------------------------------------------#
def assign_frac_id(gb):
gb.add_node_props(["frac_id"])
for g, d in gb:
if g.dim < 2:
d["frac_id"] = -1 * np.ones(g.num_cells, dtype=np.int)
if np.isclose(np.amin(np.abs(g.nodes[0, :])), 0.5) and np.isclose(
np.amax(np.abs(g.nodes[0, :])), 0.5
):
d["frac_id"] = 2 * np.ones(g.num_cells, dtype=np.int)
if np.isclose(np.amin(np.abs(g.nodes[1, :])), 0) and np.isclose(
np.amax(np.abs(g.nodes[1, :])), 0
):
d["frac_id"] = 1 * np.ones(g.num_cells, dtype=np.int)
if np.isclose(np.amin(np.abs(g.nodes[2, :])), 0) and np.isclose(
np.amax(np.abs(g.nodes[2, :])), 0
):
d["frac_id"] = 0 * np.ones(g.num_cells, dtype=np.int)
# ------------------------------------------------------------------------------#
def source_f0(x, y, z):
val = (
0.1
* (-0.5 - x)
* (
6 * x
- 16 * y * y
- (16 * x * x * y * y) / (x * x + y * y)
+ 48 * x * y * np.arctan2(y, x)
)
+ 0.1
* (-0.5 - x)
* (
16 * x * x
+ (16 * x * x * y * y) / (x * x + y * y)
+ 48 * x * y * np.arctan2(y, x)
)
+ (1 / 5.0)
* (
-3 * x * x
+ 8 * x * y * y
- 16 * x * x * y * np.arctan2(y, x)
- 8 * y * (x * x + y * y) * np.arctan2(y, x)
)
)
return -val
# ------------------------------------------------------------------------------#
def source_f1(x, y, z):
val = (
(3 / 5.0) * (-0.5 - x) * x
- (3 * x * x) / 5.0
- (24 / 5.0) * np.pi * (-0.5 - x) * x * np.abs(z)
+ (24 / 5.0) * np.pi * x * x * np.abs(z)
)
return -val
# ------------------------------------------------------------------------------#
def source_f2(x, y, z):
val = (
2 * (-1 + y) * y * (1 + y)
+ 2 * (-1 + y) * (-1 + z) * z
+ 2 * y * (-1 + z) * z
+ 2 * (1 + y) * (-1 + z) * z
)
return -val
# ------------------------------------------------------------------------------#
source_f = [source_f0, source_f1, source_f2]
# ------------------------------------------------------------------------------#
def sol_f0(x, y, z):
return ((-0.1) * (0.5 + x)) * (
x * x * x + 8 * x * y * (x * x + y * y) * np.arctan2(y, x)
)
# ------------------------------------------------------------------------------#
def sol_f1(x, y, z):
return (1 / 10.0) * (-0.5 - x) * x * x * x - np.abs(z) * np.pi * (4 / 5.0) * (
-0.5 - x
) * x * x * x
# ------------------------------------------------------------------------------#
def sol_f2(x, y, z):
return y * (y - 1) * (y + 1) * z * (z - 1)
# ------------------------------------------------------------------------------#
sol_f = [sol_f0, sol_f1, sol_f2]
# ------------------------------------------------------------------------------#
def vel_f0(x, y, z):
u = np.array(
[
0.1
* (-0.5 - x)
* (
3 * x ** 2
- 8 * x * y ** 2
+ 16 * x ** 2 * y * np.arctan2(y, x)
+ 8 * y * (x ** 2 + y ** 2) * np.arctan2(y, x)
)
+ 0.1 * (-x ** 3 - 8 * x * y * (x ** 2 + y ** 2) * np.arctan2(y, x)),
0.1
* (-0.5 - x)
* (
8 * x ** 2 * y
+ 16 * x * y ** 2 * np.arctan2(y, x)
+ 8 * x * (x ** 2 + y ** 2) * np.arctan2(y, x)
),
0,
]
)
return -u
# ------------------------------------------------------------------------------#
def vel_f1(x, y, z):
u = np.array(
[
(3 / 10.0) * (-0.5 - x) * x ** 2
- x ** 3 / 10.0
- (12 / 5.0) * np.pi * (-0.5 - x) * x ** 2 * np.abs(z)
+ (4 / 5.0) * np.pi * x ** 3 * np.abs(z),
0,
-np.sign(z) * (4 / 5.0) * np.pi * (-0.5 - x) * x ** 3,
]
)
return -u
# ------------------------------------------------------------------------------#
def vel_f2(x, y, z):
u = np.array(
[
0,
(-1 + y) * y * (-1 + z) * z
+ (-1 + y) * (1 + y) * (-1 + z) * z
+ y * (1 + y) * (-1 + z) * z,
(-1 + y) * y * (1 + y) * (-1 + z) + (-1 + y) * y * (1 + y) * z,
]
)
return -u
# ------------------------------------------------------------------------------#
vel_f = [vel_f0, vel_f1, vel_f2]
# ------------------------------------------------------------------------------#
def perm(x, y, z):
return 1
# ------------------------------------------------------------------------------#
def error_pressure(gb, p_name):
error = 0
for g, d in gb:
if g.dim < 2:
d["err"] = np.zeros(g.num_cells)
continue
frac_id = d["frac_id"][0]
sol = np.array([sol_f[frac_id](*pt) for pt in g.cell_centers.T])
d["err"] = np.abs(d[p_name] - sol)
error += np.sum(np.power(d["err"], 2) * g.cell_volumes)
return np.sqrt(error)
# ------------------------------------------------------------------------------#
def error_discharge(gb, P0u_name):
error = np.zeros(3)
for g, d in gb:
if g.dim < 2:
continue
frac_id = d["frac_id"][0]
sol = np.array([vel_f[frac_id](*pt) for pt in g.cell_centers.T]).T
err = np.abs(d[P0u_name] - sol)
for i in np.arange(3):
error[i] += np.sum(np.power(err[i, :], 2) * g.cell_volumes)
return np.sqrt(np.sum(error))
# ------------------------------------------------------------------------------#