You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
93 lines
3.1 KiB
93 lines
3.1 KiB
3 years ago
|
"""Solve nonlinear corrections to Darcy flow
|
||
|
|
"""
|
||
|
|
|
||
|
|
import dolfin as df
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
import numpy as np
|
||
|
|
import matplotlib.ticker as ticker
|
||
|
|
import sys
|
||
|
|
import os
|
||
|
|
from time import time
|
||
|
|
|
||
|
|
|
||
|
|
def solve_nonlinear_poisson(input, alpha1, alpha2, save_dir):
|
||
|
|
if not os.path.exists(save_dir):
|
||
|
|
os.makedirs(save_dir)
|
||
|
|
perm = input
|
||
|
|
flux_order = 3
|
||
|
|
ngy, ngx = perm.shape[0], perm.shape[1]
|
||
|
|
|
||
|
|
# Create mesh and define function space
|
||
|
|
mesh = df.UnitSquareMesh(ngy-1, ngx-1)
|
||
|
|
K_CG = df.FunctionSpace(mesh, "Lagrange", 1)
|
||
|
|
|
||
|
|
K = df.Function(K_CG)
|
||
|
|
ordering = df.dof_to_vertex_map(K_CG)
|
||
|
|
K.vector()[:] = perm.flatten(order='C')[ordering]
|
||
|
|
|
||
|
|
def boundary(x, on_boundary):
|
||
|
|
return x[0] < df.DOLFIN_EPS or x[0] > 1.0 - df.DOLFIN_EPS
|
||
|
|
left = df.CompiledSubDomain("near(x[0], 0.0) && on_boundary")
|
||
|
|
right = df.CompiledSubDomain("near(x[0], 1.0) && on_boundary")
|
||
|
|
top = df.CompiledSubDomain("near(x[1], 1.0) && on_boundary")
|
||
|
|
bottom = df.CompiledSubDomain("near(x[1], 0.0) && on_boundary")
|
||
|
|
boundaries = df.MeshFunction("size_t", mesh, mesh.topology().dim() - 1, 0)
|
||
|
|
# boundaries.set_all(0)
|
||
|
|
left.mark(boundaries, 1)
|
||
|
|
top.mark(boundaries, 2)
|
||
|
|
right.mark(boundaries, 3)
|
||
|
|
bottom.mark(boundaries, 4)
|
||
|
|
ds = df.Measure("ds", domain=mesh, subdomain_data=boundaries)
|
||
|
|
|
||
|
|
# Discontinuous Raviart-Thomas
|
||
|
|
DRT = df.FiniteElement("DRT", mesh.ufl_cell(), flux_order)
|
||
|
|
# Lagrange
|
||
|
|
CG = df.FiniteElement("CG", mesh.ufl_cell(), flux_order + 1)
|
||
|
|
W = df.FunctionSpace(mesh, DRT * CG)
|
||
|
|
|
||
|
|
ww = df.Function(W)
|
||
|
|
sigma, u = df.split(ww)
|
||
|
|
tau, v = df.TestFunctions(W)
|
||
|
|
dw = df.TrialFunction(W)
|
||
|
|
|
||
|
|
# Define boundary condition
|
||
|
|
gamma = df.Expression("1.0 - x[0]", degree=1)
|
||
|
|
bc = df.DirichletBC(W.sub(1), gamma, boundary)
|
||
|
|
g = df.Constant(0.0)
|
||
|
|
f = df.Constant(0.0)
|
||
|
|
|
||
|
|
def flux(sigma):
|
||
|
|
s1 = sigma[0]
|
||
|
|
s2 = sigma[1]
|
||
|
|
nonlinear1 = alpha1 * df.sqrt(K) * df.as_vector([s1 ** 2, s2 ** 2])
|
||
|
|
nonlinear2 = alpha2 * K * df.as_vector([s1 ** 3, s2 ** 3])
|
||
|
|
nonlinear = nonlinear1 + nonlinear2
|
||
|
|
return nonlinear
|
||
|
|
|
||
|
|
F = (df.dot(sigma, tau) + df.dot(K * df.grad(u), tau) + df.dot(flux(sigma), tau)\
|
||
|
|
+ df.dot(sigma, df.grad(v)) + f * v) * df.dx + g * v * ds(2) + g * v * ds(4)
|
||
|
|
J = df.derivative(F, ww, dw)
|
||
|
|
|
||
|
|
# Compute solution
|
||
|
|
problem = df.NonlinearVariationalProblem(F, ww, bc, J)
|
||
|
|
solver = df.NonlinearVariationalSolver(problem)
|
||
|
|
prm = solver.parameters
|
||
|
|
prm['newton_solver']['absolute_tolerance'] = 1E-8
|
||
|
|
prm['newton_solver']['relative_tolerance'] = 1E-6
|
||
|
|
prm['newton_solver']['maximum_iterations'] = 10
|
||
|
|
prm['newton_solver']['relaxation_parameter'] = 1.0
|
||
|
|
tic = time()
|
||
|
|
solver.solve()
|
||
|
|
print(f'time taken {time()-tic} seconds')
|
||
|
|
|
||
|
|
(sigma_, u_) = ww.split()
|
||
|
|
|
||
|
|
u_mat = u_.compute_vertex_values(mesh).reshape(64, 64)
|
||
|
|
grad_u = sigma_.compute_vertex_values(mesh)
|
||
|
|
sigma1 = grad_u[:4096].reshape(64, 64)
|
||
|
|
sigma2 = grad_u[4096:].reshape(64, 64)
|
||
|
|
output = np.stack((u_mat, sigma1, sigma2))
|
||
|
|
print('output shape: {output.shape}')
|
||
|
|
return output
|
||
|
|
|