def assemble_blockwise_matrix_BDF1(dt, ux_n1, uy_n1):
S11 = assemble.u_gradv_w_p1(topo_u, x_u, y_u, ux_n1, uy_n1)
D11 = M + dt*K + dt*S11
D22 = M + dt*K + dt*S11
S12 = sparse.csc_matrix((ndofs_u, ndofs_u))
S21 = sparse.csc_matrix((ndofs_u, ndofs_u))
(D11, D22) = apply_mat_bc(D11, D22)
#### assembly of Navier-Stokes system
mat = sparse.vstack([
sparse.hstack([D11, S12, -dt*BT1, sparse.csc_matrix((ndofs_u, 1))]),
sparse.hstack([S21, D22, -dt*BT2, sparse.csc_matrix((ndofs_u, 1))]),
sparse.hstack([-B, sparse.csc_matrix((ndofs_p,ndofs_p)), mean_p.transpose()]),
sparse.hstack([sparse.csc_matrix((1, 2*ndofs_u)), mean_p, sparse.csc_matrix((1,1))])
], "csc")
return mat
def assemble_blockwise_matrix_BDF2():
S11 = assemble.u_gradv_w_p1(topo_u, x_u, y_u, ux_n1, uy_n1)
D11 = 1.5 * ph.rho_fluid / ph.dt * M11 + ph.nu * A11 + ph.rho_fluid * S11
D22 = 1.5 * ph.rho_fluid / ph.dt * M11 + ph.nu * A11 + ph.rho_fluid * S11
S12 = sparse.csr_matrix((ndofs_u, ndofs_u))
S21 = sparse.csr_matrix((ndofs_u, ndofs_u))
(D11, D22) = apply_bc_mat(D11, D22)
#### assembly of Navier-Stokes system
mat = sparse.vstack(
[
sparse.hstack([D11, S12, -BT1
]), #, sparse.csr_matrix((ndofs_u, 1))]),
sparse.hstack([S21, D22, -BT2
]), #, sparse.csr_matrix((ndofs_u, 1))]),
sparse.hstack([-B, sparse.csr_matrix(
(ndofs_p, ndofs_p))]) #, mean_p.transpose()]),
# sparse.hstack([sparse.csr_matrix((1, 2*ndofs_u)), mean_p, sparse.csr_matrix((1,1))])
],
"csr")
return mat
max_iter = 10
residuals = np.zeros((len(ph.stampa), max_iter))
#### start time steppig procedure
for cn_time in range(0, len(ph.stampa)):
step_t0 = time.time()
t_sol = 0
u_n1 = u_n
ux_n1 = ux_n
uy_n1 = uy_n
p_n1 = p_n
if ph.time_integration == 'BDF1':
force = assemble_blockwise_force_BDF1()
mat = assemble_blockwise_matrix_BDF1()
elif ph.time_integration == 'Theta' or cn_time == 0:
S11 = assemble.u_gradv_w_p1(topo_u, x_u, y_u, ux_n1, uy_n1)
force = assemble_blockwise_force_Theta(S11)
mat = assemble_blockwise_matrix_Theta(S11)
else:
force = assemble_blockwise_force_BDF2()
mat = assemble_blockwise_matrix_BDF2()
for k in range(max_iter):
sol = sp_la.spsolve(mat, force)
u_n1 = np.reshape(sol[0:2 * ndofs_u], u_n.shape)
p_n1 = np.reshape(sol[2 * ndofs_u:2 * ndofs_u + ndofs_p], (ndofs_p, 1))
ux_n1 = np.reshape(u_n1[0:ndofs_u], ux_n.shape)
uy_n1 = np.reshape(u_n1[ndofs_u:2 * ndofs_u], uy_n.shape)
if ph.time_integration == 'BDF1':
sy_asmbl = 2*sy_n - sy_n_old
elif ph.time_integration == 'CN':
ux_asmbl = 1.5*ux_n - 0.5*ux_n_old
uy_asmbl = 1.5*uy_n - 0.5*uy_n_old
sx_asmbl = 1.5*sx_n - 0.5*sx_n_old
sy_asmbl = 1.5*sy_n - 0.5*sy_n_old
else:
ux_asmbl = ux_n
uy_asmbl = uy_n
sx_asmbl = sx_n
sy_asmbl = sy_n
(G, GT, GT11, GT22) = assemble_kinematic_coupling(sx_asmbl, sy_asmbl)
(H, HT, HT11, HT22) = assemble_kinematic_coupling(sx_n, sy_n)
if(ph.fluid_behavior == "Navier-Stokes"):
S11 = ph.rho_fluid*assemble.u_gradv_w_p1(topo_u, x_u, y_u, ux_asmbl, uy_asmbl)
T11 = ph.rho_fluid*assemble.u_gradv_w_p1(topo_u, x_u, y_u, ux_n, uy_n)
else:
S11 = sparse.csc_matrix((ndofs_u, ndofs_u))
T11 = S11
###Assemble linear system and solve
if ph.time_integration == 'BDF1':
mat = assemble_blockwise_matrix_BDF1(S11)
force = assemble_blockwise_force_BDF1(ux_n, uy_n, dx_n, dy_n)
elif ph.time_integration == 'CN':
mat = assemble_blockwise_matrix_CN(S11)
force = assemble_blockwise_force_CN(ux_n, uy_n, u_n, p_n, dx_n, dy_n, l_n)
elif ph.time_integration == 'TR':
mat = assemble_blockwise_matrix_TR(S11)
force = assemble_blockwise_force_TR(ux_n, uy_n, u_n, p_n, dx_n, dy_n, l_n)