v = TestFunction(V)
F = u * v / dt * dx + alpha * dot(grad(u), grad(v)) * dx - u_n * v / dt * dx
# apply constant Dirichlet boundary condition at bottom edge
# apply Dirichlet boundary condition on coupling interface
bcs = [DirichletBC(V, coupling_expression, coupling_boundary), DirichletBC(V, u_D, bottom_boundary)]
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
F_known_u = u_np1 * v / dt * dx + alpha * dot(grad(u_np1), grad(v)) * dx - u_n * v / dt * dx
t = 0
u_D.t = t + dt
file_out = File("Solid/VTK/%s.pvd" % precice.get_participant_name())
n = 0
while precice.is_coupling_ongoing():
if precice.is_action_required(precice.action_write_iteration_checkpoint()): # write checkpoint
precice.store_checkpoint(u_n, t, n)
read_data = precice.read_data()
# Update the coupling expression with the new read data
precice.update_coupling_expression(coupling_expression, read_data)
dt.assign(np.min([fenics_dt, precice_dt]))
# Compute solution
raise Exception("Boundary markers are not implemented yet")
# return dot(coupling_bc_expression, v) * dolfin.dss(boundary_marker)
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
u_np1.rename("Temperature", "")
t = 0
# reference solution at t=0
u_ref = interpolate(u_D, V)
u_ref.rename("reference", " ")
# Generating output files
temperature_out = File("out/%s.pvd" % precice.get_participant_name())
ref_out = File("out/ref%s.pvd" % precice.get_participant_name())
error_out = File("out/error%s.pvd" % precice.get_participant_name())
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
temperature_out << u_n
ref_out << u_ref
error_total, error_pointwise = compute_errors(u_n, u_ref, V)
error_out << error_pointwise
# set t_1 = t_0 + dt, this gives u_D^1
u_D.t = t + dt(
0) # call dt(0) to evaluate FEniCS Constant. Todo: is there a better way?