def test_two_blocks_with_restriction(mesh, restriction, FunctionSpaces,
BlockBCs):
(FunctionSpace1, FunctionSpace2) = FunctionSpaces
V1 = FunctionSpace1(mesh)
V2 = FunctionSpace2(mesh)
block_V = BlockFunctionSpace([V1, V2], restrict=restriction)
block_form = get_rhs_block_form_2(block_V)
block_bcs = BlockBCs(block_V)
(rhs, block_rhs) = assemble_and_block_assemble_vector(block_form)
apply_bc_and_block_bc_vector(rhs, block_rhs, block_bcs)
assert_block_vectors_equal(rhs, block_rhs, block_V)
(rhs, block_rhs) = assemble_and_block_assemble_vector(block_form)
(function, block_function) = apply_bc_and_block_bc_vector_non_linear(
rhs, block_rhs, block_bcs, block_V)
assert_block_vectors_equal(rhs, block_rhs, block_V)
assert_block_functions_equal(function, block_function, block_V)
def test_single_block_no_restriction_from_block_element(mesh, Element):
V_element = Element(mesh)
V = FunctionSpace(mesh, V_element)
block_V_element = BlockElement(V_element)
block_V = BlockFunctionSpace(mesh, block_V_element)
assert_dof_map_single_block_no_restriction(V, block_V)
def test_single_block_no_restriction_from_list(mesh, FunctionSpace):
V = FunctionSpace(mesh)
block_V = BlockFunctionSpace([V])
assert_dof_map_single_block_no_restriction(V, block_V)
def test_two_blocks_with_restriction_from_list(mesh, restriction, FunctionSpaces):
(FunctionSpace1, FunctionSpace2) = FunctionSpaces
V1 = FunctionSpace1(mesh)
V2 = FunctionSpace2(mesh)
block_V = BlockFunctionSpace([V1, V2], restrict=restriction)
assert_dof_map_test_two_blocks_with_restriction(V1, V2, block_V)
def test_single_block_with_restriction(mesh, restriction, FunctionSpace):
V = FunctionSpace(mesh)
block_V = BlockFunctionSpace([V], restrict=[restriction])
functions = get_list_of_functions_1(block_V)
assert_functions_manipulations(functions, block_V)
def initialization(mesh, subdomains, boundaries):
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
UCG = VectorElement("CG", mesh.ufl_cell(), 2)
BDM = FiniteElement("BDM", mesh.ufl_cell(), 1)
PDG = FiniteElement("DG", mesh.ufl_cell(), 0)
UCG_F = FunctionSpace(mesh, UCG)
BDM_F = FunctionSpace(mesh, BDM)
PDG_F = FunctionSpace(mesh, PDG)
W = BlockFunctionSpace([BDM_F, PDG_F], restrict=[None, None])
U = BlockFunctionSpace([UCG_F])
I = Identity(mesh.topology().dim())
C_cg = FiniteElement("CG", mesh.ufl_cell(), 1)
C_dg = FiniteElement("DG", mesh.ufl_cell(), 0)
mini = C_cg + C_dg
C = FunctionSpace(mesh, mini)
C = BlockFunctionSpace([C])
#TODO
solution0_h = BlockFunction(W)
solution0_m = BlockFunction(U)
solution0_c = BlockFunction(C)
solution1_h = BlockFunction(W)
solution1_m = BlockFunction(U)
solution1_c = BlockFunction(C)
solution2_h = BlockFunction(W)
solution2_m = BlockFunction(U)
solution2_c = BlockFunction(C)
solution_h = BlockFunction(W)
solution_m = BlockFunction(U)
solution_c = BlockFunction(C)
## mechanics
# 0 properties
alpha1 = 0.74
K1 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha_0 = Function(PM)
K_0 = Function(PM)
nu_0 = Function(PM)
alpha_0 = init_scalar_parameter(alpha_0, alpha_values[0], 500, subdomains)
K_0 = init_scalar_parameter(K_0, K_values[0], 500, subdomains)
nu_0 = init_scalar_parameter(nu_0, nu_values[0], 500, subdomains)
alpha_0 = init_scalar_parameter(alpha_0, alpha_values[1], 501, subdomains)
K_0 = init_scalar_parameter(K_0, K_values[1], 501, subdomains)
nu_0 = init_scalar_parameter(nu_0, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l_0, lmbda_l_0, Ks_0, K_0 = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K_0,nu_0,alpha_0,K_0)
# n-1 properties
alpha1 = 0.74
K1 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha_1 = Function(PM)
K_1 = Function(PM)
nu_1 = Function(PM)
alpha_1 = init_scalar_parameter(alpha_1, alpha_values[0], 500, subdomains)
K_1 = init_scalar_parameter(K_1, K_values[0], 500, subdomains)
nu_1 = init_scalar_parameter(nu_1, nu_values[0], 500, subdomains)
alpha_1 = init_scalar_parameter(alpha_1, alpha_values[1], 501, subdomains)
K_1 = init_scalar_parameter(K_1, K_values[1], 501, subdomains)
nu_1 = init_scalar_parameter(nu_1, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l_1, lmbda_l_1, Ks_1, K_1 = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K_1,nu_1,alpha_1,K_0)
# n properties
alpha1 = 0.74
K2 = 8.4 * 1000.e6
nu1 = 0.18
alpha2 = 0.74
K2 = 8.4 * 1000.e6
nu2 = 0.18
alpha_values = [alpha1, alpha2]
K_values = [K1, K2]
nu_values = [nu1, nu2]
alpha = Function(PM)
K = Function(PM)
nu = Function(PM)
alpha = init_scalar_parameter(alpha, alpha_values[0], 500, subdomains)
K = init_scalar_parameter(K, K_values[0], 500, subdomains)
nu = init_scalar_parameter(nu, nu_values[0], 500, subdomains)
alpha = init_scalar_parameter(alpha, alpha_values[1], 501, subdomains)
K = init_scalar_parameter(K, K_values[1], 501, subdomains)
nu = init_scalar_parameter(nu, nu_values[1], 501, subdomains)
K_mult_min = 1.0
K_mult_max = 1.0
mu_l, lmbda_l, Ks, K = \
bulk_modulus_update(mesh,solution0_c[0],K_mult_min,K_mult_max,K,nu,alpha,K_0)
## flow
# 0 properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf_0 = Function(PM)
phi_0 = Function(PM)
rho_0 = Function(PM)
mu_0 = Function(PM)
k_0 = Function(TM)
cf_0 = init_scalar_parameter(cf_0, cf_values[0], 500, subdomains)
phi_0 = init_scalar_parameter(phi_0, phi_values[0], 500, subdomains)
rho_0 = init_scalar_parameter(rho_0, rho_values[0], 500, subdomains)
mu_0 = init_scalar_parameter(mu_0, mu_values[0], 500, subdomains)
k_0 = init_tensor_parameter(k_0, k_values[0], 500, subdomains,
mesh.topology().dim())
cf_0 = init_scalar_parameter(cf_0, cf_values[1], 501, subdomains)
phi_0 = init_scalar_parameter(phi_0, phi_values[1], 501, subdomains)
rho_0 = init_scalar_parameter(rho_0, rho_values[1], 501, subdomains)
mu_0 = init_scalar_parameter(mu_0, mu_values[1], 501, subdomains)
k_0 = init_tensor_parameter(k_0, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k_0 = init_from_file_parameter(k_0,0.,0.,filename)
# n-1 properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf_1 = Function(PM)
phi_1 = Function(PM)
rho_1 = Function(PM)
mu_1 = Function(PM)
k_1 = Function(TM)
cf_1 = init_scalar_parameter(cf_1, cf_values[0], 500, subdomains)
phi_1 = init_scalar_parameter(phi_1, phi_values[0], 500, subdomains)
rho_1 = init_scalar_parameter(rho_1, rho_values[0], 500, subdomains)
mu_1 = init_scalar_parameter(mu_1, mu_values[0], 500, subdomains)
k_1 = init_tensor_parameter(k_1, k_values[0], 500, subdomains,
mesh.topology().dim())
cf_1 = init_scalar_parameter(cf_1, cf_values[1], 501, subdomains)
phi_1 = init_scalar_parameter(phi_1, phi_values[1], 501, subdomains)
rho_1 = init_scalar_parameter(rho_1, rho_values[1], 501, subdomains)
mu_1 = init_scalar_parameter(mu_1, mu_values[1], 501, subdomains)
k_1 = init_tensor_parameter(k_1, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k_1 = init_from_file_parameter(k_1,0.,0.,filename)
# n properties
cf1 = 1e-10
phi1 = 0.2
rho1 = 1000.0
mu1 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k1 = np.array([kx, 0., 0., ky])
cf2 = 1e-10
phi2 = 0.2
rho2 = 1000.0
mu2 = 1.
kx = 8.802589710965712e-10
ky = 8.802589710965712e-11
k2 = np.array([kx, 0., 0., ky])
cf_values = [cf1, cf2]
phi_values = [phi1, phi2]
rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
k_values = [k1, k2]
cf = Function(PM)
phi = Function(PM)
rho = Function(PM)
mu = Function(PM)
k = Function(TM)
cf = init_scalar_parameter(cf, cf_values[0], 500, subdomains)
phi = init_scalar_parameter(phi, phi_values[0], 500, subdomains)
rho = init_scalar_parameter(rho, rho_values[0], 500, subdomains)
mu = init_scalar_parameter(mu, mu_values[0], 500, subdomains)
k = init_tensor_parameter(k, k_values[0], 500, subdomains,
mesh.topology().dim())
cf = init_scalar_parameter(cf, cf_values[1], 501, subdomains)
phi = init_scalar_parameter(phi, phi_values[1], 501, subdomains)
rho = init_scalar_parameter(rho, rho_values[1], 501, subdomains)
mu = init_scalar_parameter(mu, mu_values[1], 501, subdomains)
k = init_tensor_parameter(k, k_values[1], 501, subdomains,
mesh.topology().dim())
#filename = "perm4.csv"
#k = init_from_file_parameter(k,0.,0.,filename)
### transport
# 0
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d_0 = Function(TM)
d_0 = init_tensor_parameter(d_0, d_values[0], 500, subdomains,
mesh.topology().dim())
d_0 = init_tensor_parameter(d_0, d_values[1], 501, subdomains,
mesh.topology().dim())
# n-1
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d_1 = Function(TM)
d_1 = init_tensor_parameter(d_1, d_values[0], 500, subdomains,
mesh.topology().dim())
d_1 = init_tensor_parameter(d_1, d_values[1], 501, subdomains,
mesh.topology().dim())
# n
dx1 = 1e-12
dy1 = 1e-12
d1 = np.array([dx1, 0., 0., dy1])
dx2 = 1e-12
dy2 = 1e-12
d2 = np.array([dx2, 0., 0., dy2])
d_values = [d1, d2]
d = Function(TM)
d = init_tensor_parameter(d, d_values[0], 500, subdomains,
mesh.topology().dim())
d = init_tensor_parameter(d, d_values[1], 501, subdomains,
mesh.topology().dim())
####initialization
# initial
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution0_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution0_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution0_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution0_c.sub(0), c0_project)
# n - 1
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution1_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution1_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution1_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution1_c.sub(0), c0_project)
# n - 2
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution2_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution2_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution2_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution2_c.sub(0), c0_project)
# n
u_0 = Constant((0.0, 0.0))
u_0_project = project(u_0, U[0])
assign(solution_m.sub(0), u_0_project)
p_0 = Constant(1.e6)
p_0_project = project(p_0, W[1])
assign(solution_h.sub(1), p_0_project)
# v_0 = Constant((0.0, 0.0))
# v_0_project = project(v_0, W[0])
# assign(solution_h.sub(0), v_0_project)
c0 = c_sat_cal(1.e6, 20.)
c0_project = project(c0, C[0])
assign(solution_c.sub(0), c0_project)
###iterative parameters
phi_it = Function(PM)
assign(phi_it, phi_0)
print('c_sat', c_sat_cal(1.0e8, 20.))
c_sat = c_sat_cal(1.0e8, 20.)
c_sat = project(c_sat, PM)
c_inject = Constant(0.0)
c_inject = project(c_inject, PM)
mu_c1_1 = 1.e-4
mu_c2_1 = 5.e-0
mu_c1_2 = 1.e-4
mu_c2_2 = 5.e-0
mu_c1_values = [mu_c1_1, mu_c1_2]
mu_c2_values = [mu_c2_1, mu_c2_2]
mu_c1 = Function(PM)
mu_c2 = Function(PM)
mu_c1 = init_scalar_parameter(mu_c1, mu_c1_values[0], 500, subdomains)
mu_c2 = init_scalar_parameter(mu_c2, mu_c2_values[0], 500, subdomains)
mu_c1 = init_scalar_parameter(mu_c1, mu_c1_values[1], 501, subdomains)
mu_c2 = init_scalar_parameter(mu_c2, mu_c2_values[1], 501, subdomains)
coeff_for_perm_1 = 22.2
coeff_for_perm_2 = 22.2
coeff_for_perm_values = [coeff_for_perm_1, coeff_for_perm_2]
coeff_for_perm = Function(PM)
coeff_for_perm = init_scalar_parameter(coeff_for_perm,
coeff_for_perm_values[0], 500,
subdomains)
coeff_for_perm = init_scalar_parameter(coeff_for_perm,
coeff_for_perm_values[1], 501,
subdomains)
solutionIt_h = BlockFunction(W)
return solution0_m, solution0_h, solution0_c \
,solution1_m, solution1_h, solution1_c \
,solution2_m, solution2_h, solution2_c \
,solution_m, solution_h, solution_c \
,alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0 \
,alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1 \
,alpha, K, mu_l, lmbda_l, Ks \
,cf_0, phi_0, rho_0, mu_0, k_0 \
,cf_1, phi_1, rho_1, mu_1, k_1 \
,cf, phi, rho, mu, k \
,d_0, d_1, d, I \
,phi_it, solutionIt_h, mu_c1, mu_c2 \
,nu_0, nu_1, nu, coeff_for_perm \
,c_sat, c_inject
def transport_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
d_0, d_1, d_t,
vel_c, p_con, A_0, Temp, c_extrapolate):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
C_cg = FiniteElement("CG", mesh.ufl_cell(), 1)
C_dg = FiniteElement("DG", mesh.ufl_cell(), 0)
mini = C_cg + C_dg
C = FunctionSpace(mesh, mini)
C = BlockFunctionSpace([C])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc / fc
h_avg = (vc('+') + vc('-')) / (2 * avg(fc))
penalty1 = Constant(1.0)
tau = Function(PM)
tau = tau_cal(tau, phi, -0.5)
tuning_para = 0.25
vel_norm = (dot(vel_c, n) + abs(dot(vel_c, n))) / 2.0
cell_size = CellDiameter(mesh)
vnorm = sqrt(dot(vel_c, vel_c))
I = Identity(mesh.topology().dim())
d_eff = Function(TM)
d_eff = diff_coeff_cal_rev(d_eff, d_0, tau,
phi) + tuning_para * cell_size * vnorm * I
monitor_dt = dt
# Define variational problem
dc, = BlockTrialFunction(C)
dc_dot, = BlockTrialFunction(C)
psic, = BlockTestFunction(C)
block_c = BlockFunction(C)
c, = block_split(block_c)
block_c_dot = BlockFunction(C)
c_dot, = block_split(block_c_dot)
theta = -1.0
a_time = phi * rho * inner(c_dot, psic) * dx
a_dif = dot(rho*d_eff*grad(c),grad(psic))*dx \
- dot(avg_w(rho*d_eff*grad(c),weight_e(rho*d_eff,n)), jump(psic, n))*dS \
+ theta*dot(avg_w(rho*d_eff*grad(psic),weight_e(rho*d_eff,n)), jump(c, n))*dS \
+ penalty1/h_avg*k_e(rho*d_eff,n)*dot(jump(c, n), jump(psic, n))*dS
a_adv = -dot(rho*vel_c*c,grad(psic))*dx \
+ dot(jump(psic), rho('+')*vel_norm('+')*c('+') - rho('-')*vel_norm('-')*c('-') )*dS \
+ dot(psic, rho*vel_norm*c)*ds(3)
R_c = R_c_cal(c_extrapolate, p_con, Temp)
c_D1 = Constant(0.5)
rhs_c = R_c * A_s_cal(phi, phi_0, A_0) * psic * dx - dot(
rho * phi * vel_c, n) * c_D1 * psic * ds(1)
r_u = [a_dif + a_adv]
j_u = block_derivative(r_u, [c], [dc])
r_u_dot = [a_time]
j_u_dot = block_derivative(r_u_dot, [c_dot], [dc_dot])
r = [r_u_dot[0] + r_u[0] - rhs_c]
# this part is not applied.
exact_solution_expression1 = Expression("1.0",
t=0,
element=C[0].ufl_element())
def bc(t):
p5 = DirichletBC(C.sub(0),
exact_solution_expression1,
boundaries,
1,
method="geometric")
return BlockDirichletBC([p5])
# Define problem wrapper
class ProblemWrapper(object):
def set_time(self, t):
pass
# Residual and jacobian functions
def residual_eval(self, t, solution, solution_dot):
return r
def jacobian_eval(self, t, solution, solution_dot,
solution_dot_coefficient):
return [[
Constant(solution_dot_coefficient) * j_u_dot[0, 0] + j_u[0, 0]
]]
# Define boundary condition
def bc_eval(self, t):
pass
# Define initial condition
def ic_eval(self):
return solution0
# Define custom monitor to plot the solution
def monitor(self, t, solution, solution_dot):
pass
problem_wrapper = ProblemWrapper()
(solution, solution_dot) = (block_c, block_c_dot)
solver = TimeStepping(problem_wrapper, solution, solution_dot)
solver.set_parameters({
"initial_time": t_start,
"time_step_size": dt,
"monitor": {
"time_step_size": monitor_dt,
},
"final_time": T,
"exact_final_time": "stepover",
"integrator_type": integrator_type,
"problem_type": "linear",
"linear_solver": "mumps",
"report": True
})
export_solution = solver.solve()
return export_solution, T
def m_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
pressure_freeze):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
C = VectorFunctionSpace(mesh, "CG", 2)
C = BlockFunctionSpace([C])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc/fc
h_avg = (vc('+') + vc('-'))/(2*avg(fc))
monitor_dt = dt
f_stress_x = Constant(-1.e3)
f_stress_y = Constant(-20.0e6)
f = Constant((0.0, 0.0)) #sink/source for displacement
I = Identity(mesh.topology().dim())
# Define variational problem
psiu, = BlockTestFunction(C)
block_u = BlockTrialFunction(C)
u, = block_split(block_u)
w = BlockFunction(C)
theta = -1.0
a_time = inner(-alpha*pressure_freeze*I,sym(grad(psiu)))*dx #quasi static
a = inner(2*mu_l*strain(u)+lmbda_l*div(u)*I, sym(grad(psiu)))*dx
rhs_a = inner(f,psiu)*dx \
+ dot(f_stress_y*n,psiu)*ds(2)
r_u = [a]
#DirichletBC
bcd1 = DirichletBC(C.sub(0).sub(0), 0.0, boundaries, 1) # No normal displacement for solid on left side
bcd3 = DirichletBC(C.sub(0).sub(0), 0.0, boundaries, 3) # No normal displacement for solid on right side
bcd4 = DirichletBC(C.sub(0).sub(1), 0.0, boundaries, 4) # No normal displacement for solid on bottom side
bcs = BlockDirichletBC([bcd1,bcd3,bcd4])
AA = block_assemble([r_u])
FF = block_assemble([rhs_a - a_time])
bcs.apply(AA)
bcs.apply(FF)
block_solve(AA, w.block_vector(), FF, "mumps")
export_solution = w
return export_solution, T
boundaries = MeshFunction("size_t", mesh, "data/biot_2mat_facet_region.xml")
for discretization in ("DG", "EG"):
# Block function space
V_element = VectorElement("CG", mesh.ufl_cell(), 2)
if discretization == "DG":
Q_element = FiniteElement("DG", mesh.ufl_cell(), 1)
W_element = BlockElement(V_element, Q_element)
elif discretization == "EG":
Q_element = FiniteElement("CG", mesh.ufl_cell(), 1)
D_element = FiniteElement("DG", mesh.ufl_cell(), 0)
EG_element = Q_element + D_element
W_element = BlockElement(V_element, EG_element)
else:
raise RuntimeError("Invalid discretization")
W = BlockFunctionSpace(mesh, W_element)
PM = FunctionSpace(mesh, "DG", 0)
TM = TensorFunctionSpace(mesh, "DG", 0)
I = Identity(mesh.topology().dim())
dx = Measure("dx", domain=mesh, subdomain_data=subdomains)
ds = Measure("ds", domain=mesh, subdomain_data=boundaries)
dS = Measure("dS", domain=mesh, subdomain_data=boundaries)
# Test and trial functions
vq = BlockTestFunction(W)
(v, q) = block_split(vq)
up = BlockTrialFunction(W)
(u, p) = block_split(up)
def h_linear(integrator_type, mesh, subdomains, boundaries, t_start, dt, T, solution0, \
alpha_0, K_0, mu_l_0, lmbda_l_0, Ks_0, \
alpha_1, K_1, mu_l_1, lmbda_l_1, Ks_1, \
alpha, K, mu_l, lmbda_l, Ks, \
cf_0, phi_0, rho_0, mu_0, k_0,\
cf_1, phi_1, rho_1, mu_1, k_1,\
cf, phi, rho, mu, k, \
sigma_v_freeze, dphi_c_dt):
# Create mesh and define function space
parameters["ghost_mode"] = "shared_facet" # required by dS
dx = Measure('dx', domain=mesh, subdomain_data=subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)
BDM = FiniteElement("BDM", mesh.ufl_cell(), 1)
PDG = FiniteElement("DG", mesh.ufl_cell(), 0)
BDM_F = FunctionSpace(mesh, BDM)
PDG_F = FunctionSpace(mesh, PDG)
W = BlockFunctionSpace([BDM_F, PDG_F], restrict=[None, None])
TM = TensorFunctionSpace(mesh, 'DG', 0)
PM = FunctionSpace(mesh, 'DG', 0)
n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)
h = vc / fc
h_avg = (vc('+') + vc('-')) / (2 * avg(fc))
I = Identity(mesh.topology().dim())
monitor_dt = dt
p_outlet = 0.1e6
p_inlet = 1000.0
M_inv = phi_0 * cf + (alpha - phi_0) / Ks
# Define variational problem
trial = BlockTrialFunction(W)
dv, dp = block_split(trial)
trial_dot = BlockTrialFunction(W)
dv_dot, dp_dot = block_split(trial_dot)
test = BlockTestFunction(W)
psiv, psip = block_split(test)
block_w = BlockFunction(W)
v, p = block_split(block_w)
block_w_dot = BlockFunction(W)
v_dot, p_dot = block_split(block_w_dot)
a_time = Constant(0.0) * inner(v_dot, psiv) * dx #quasi static
# k is a function of phi
#k = perm_update_rutqvist_newton(p,p0,phi0,phi,coeff)
lhs_a = inner(dot(v, mu * inv(k)), psiv) * dx - p * div(
psiv
) * dx #+ 6.0*inner(psiv,n)*ds(2) # - inner(gravity*(rho-rho0), psiv)*dx
b_time = (M_inv + pow(alpha, 2.) / K) * p_dot * psip * dx
lhs_b = div(v) * psip * dx #div(rho*v)*psip*dx #TODO rho
rhs_v = -p_outlet * inner(psiv, n) * ds(3)
rhs_p = -alpha / K * sigma_v_freeze * psip * dx - dphi_c_dt * psip * dx
r_u = [lhs_a, lhs_b]
j_u = block_derivative(r_u, block_w, trial)
r_u_dot = [a_time, b_time]
j_u_dot = block_derivative(r_u_dot, block_w_dot, trial_dot)
r = [r_u_dot[0] + r_u[0] - rhs_v, \
r_u_dot[1] + r_u[1] - rhs_p]
def bc(t):
#bc_v = [DirichletBC(W.sub(0), (.0, .0), boundaries, 4)]
v1 = DirichletBC(W.sub(0), (1.e-4 * 2.0, 0.0), boundaries, 1)
v2 = DirichletBC(W.sub(0), (0.0, 0.0), boundaries, 2)
v4 = DirichletBC(W.sub(0), (0.0, 0.0), boundaries, 4)
bc_v = [v1, v2, v4]
return BlockDirichletBC([bc_v, None])
# Define problem wrapper
class ProblemWrapper(object):
def set_time(self, t):
pass
#g.t = t
# Residual and jacobian functions
def residual_eval(self, t, solution, solution_dot):
#print(as_backend_type(assemble(p_time - p_time_error)).vec().norm())
#print("gravity effect", as_backend_type(assemble(inner(gravity*(rho-rho0), psiv)*dx)).vec().norm())
return r
def jacobian_eval(self, t, solution, solution_dot,
solution_dot_coefficient):
return [[Constant(solution_dot_coefficient)*j_u_dot[0, 0] + j_u[0, 0], \
Constant(solution_dot_coefficient)*j_u_dot[0, 1] + j_u[0, 1]], \
[Constant(solution_dot_coefficient)*j_u_dot[1, 0] + j_u[1, 0], \
Constant(solution_dot_coefficient)*j_u_dot[1, 1] + j_u[1, 1]]]
# Define boundary condition
def bc_eval(self, t):
return bc(t)
# Define initial condition
def ic_eval(self):
return solution0
# Define custom monitor to plot the solution
def monitor(self, t, solution, solution_dot):
pass
# Solve the time dependent problem
problem_wrapper = ProblemWrapper()
(solution, solution_dot) = (block_w, block_w_dot)
solver = TimeStepping(problem_wrapper, solution, solution_dot)
solver.set_parameters({
"initial_time": t_start,
"time_step_size": dt,
"monitor": {
"time_step_size": monitor_dt,
},
"final_time": T,
"exact_final_time": "stepover",
"integrator_type": integrator_type,
"problem_type": "linear",
"linear_solver": "mumps",
"report": True
})
export_solution = solver.solve()
return export_solution, T
