[bc.apply(A1, b1) for bc in bcu]
solve(A1, u1.vector(), b1, "bicgstab", "default")
# Pressure correction
b2 = assemble(L2)
[bc.apply(A2, b2) for bc in bcp]
[bc.apply(p1.vector()) for bc in bcp]
solve(A2, p1.vector(), b2, "bicgstab", prec)
# Velocity correction
b3 = assemble(L3)
[bc.apply(A3, b3) for bc in bcu]
solve(A3, u1.vector(), b3, "bicgstab", "default")
# Move to next time step
u0.assign(u1)
t += dt
# Plot solution
plot(
u1,
mode='mesh and arrows',
text="Velocity of fluid",
cmap='jet',
scale=0.3, # unit conversion factor
scalarbar=False,
interactive=False)
pb.print()
plot()
def awefem(mesh, t, source_loc=None):
# Function space
V = FunctionSpace(mesh, "Lagrange", 1)
# Boundary condition
bc = DirichletBC(V, Constant(0), "on_boundary")
# Trial and test functions
u = TrialFunction(V)
v = TestFunction(V)
# Discretization
c = 6
dt = t[1] - t[0]
u0 = Function(V) # u0 = uN-1
u1 = Function(V) # u1 = uN1
# Variational formulation
F = (u - 2 * u1 + u0) * v * dx + (dt * c) ** 2 * dot(
grad(u + 2 * u1 + u0) / 4, grad(v) ) * dx
a, L = lhs(F), rhs(F)
# Solver
A, b = assemble_system(a, L)
solver = LUSolver(A, "mumps")
solver.parameters["symmetric"] = True
bc.apply(A, b)
# Solution
u = Function(V) # uN+1
# Source
if source_loc is None:
mesh_center = np.mean(mesh.coordinates(), axis=0)
source_loc = Point(mesh_center)
else:
source_loc = Point(source_loc)
# Time stepping
printc('\bomb Hit F1 to interrupt.', c='yellow')
pb = ProgressBar(0, len(t))
for i, t_ in enumerate(t[1:]):
pb.print()
b = assemble(L)
delta = PointSource(V, source_loc, ricker_source(t_) * dt**2)
delta.apply(b)
solver.solve(u.vector(), b)
u0.assign(u1)
u1.assign(u)
if t_>0.03:
plot(u,
warpZfactor=20, # set elevation along z
vmin=.0, # sets a minimum to the color scale
vmax=0.003,
cmap='rainbow', # the color map style
alpha=1, # transparency of the mesh
lw=0.1, # linewidth of mesh
scalarbar=None,
#lighting='plastic',
#elevation=-.3,
interactive=0) # continue execution
interactive()
# Read velocity from file
timeseries_w.retrieve(w.vector(), t)
# Solve variational problem for time step
solve(F == 0, u)
_u_1, _u_2, _u_3 = u.split()
# Update previous solution
u_n.assign(u)
# Plot solution
plot(_u_3, at=0, # draw on renderer nr.0
shape=(2,1), # two rows, one column
size='fullscreen',
cmap='bone',
scalarbar=False,
axes=0,
zoom=2,
interactive=False)
plot(_u_2, at=1,
cmap='bone',
zoom=2,
scalarbar=False,
interactive=False)
pb.print(t)
plot()