p0 = Point(x_left, y_bottom, 0)
p1 = Point(x_right, y_top, 1)
mesh = RectangleMesh(p0, p1, nx, ny)
V = FunctionSpace(mesh, 'P', 1)
V_g = VectorFunctionSpace(mesh, 'P', 1)
alpha = 1 # m^2/s, https://en.wikipedia.org/wiki/Thermal_diffusivity
k = 100 # kg * m / s^3 / K, https://en.wikipedia.org/wiki/Thermal_conductivity
# Define boundary condition
u_D = Constant('310')
u_D_function = interpolate(u_D, V)
# We will only exchange flux in y direction on coupling interface. No initialization necessary.
V_flux_y = V_g.sub(1)
coupling_boundary = TopBoundary()
bottom_boundary = BottomBoundary()
# Define initial value
u_n = interpolate(u_D, V)
u_n.rename("T", "")
# Adapter definition and initialization
precice = Adapter(adapter_config_filename="precice-adapter-config.json")
precice_dt = precice.initialize(coupling_boundary,
read_function_space=V,
write_object=V_flux_y)
alpha = 3 # parameter alpha
beta = 1.3 # parameter beta
if args.dirichlet and not args.neumann:
problem = ProblemType.DIRICHLET
domain_part = DomainPart.LEFT
elif args.neumann and not args.dirichlet:
problem = ProblemType.NEUMANN
domain_part = DomainPart.RIGHT
mesh, coupling_boundary, remaining_boundary = get_geometry(domain_part)
# Define function space using mesh
V = FunctionSpace(mesh, 'P', 2)
V_g = VectorFunctionSpace(mesh, 'P', 1)
W = V_g.sub(0).collapse()
# Define boundary conditions
u_D = Expression('1 + x[0]*x[0] + alpha*x[1]*x[1] + beta*t', degree=2, alpha=alpha, beta=beta, t=0)
u_D_function = interpolate(u_D, V)
if problem is ProblemType.DIRICHLET:
# Define flux in x direction
f_N = Expression("2 * x[0]", degree=1, alpha=alpha, t=0)
f_N_function = interpolate(f_N, W)
# Define initial value
u_n = interpolate(u_D, V)
u_n.rename("Temperature", "")
precice, precice_dt, initial_data = None, 0.0, None