return on_boundary and near(x[0], Length)
def exact_solution(domain):
P7 = VectorElement("Lagrange", "triangle", degree=8, dim=2)
P2 = FiniteElement("Lagrange", "triangle", 3)
coeff = (P_inlet-P_outlet)/(2*Length*visc)
u_exact = Expression(("C*x[1]*(H - x[1])", "0.0"), C=coeff,H=Height, element=P7, domain=domain)
p_exact = Expression("dP-dP/L*x[0]", dP=(P_inlet-P_outlet), L=Length, element=P2, domain=domain)
return u_exact, p_exact
# 1. Mesh from fenics
nx=4
mesh = RectangleMesh(Point(0,0), Point(Length, Height), int(nx*Length), nx, "right")
zero_vec = np.zeros(mesh.geometry().dim())
# Define boundaries
mark = {"Internal":0,"wall": 98,"inlet": 99,"outlet": 100 }
boundaries = MeshFunction('size_t', mesh, mesh.topology().dim() - 1)
boundaries.set_all(mark["Internal"])
wall=Noslip()
wall.mark(boundaries, mark["wall"])
left = Left()
left.mark(boundaries, mark["inlet"])
right = Right()
right.mark(boundaries, mark["outlet"])
ds = Measure('ds',domain=mesh,subdomain_data=boundaries)
n = FacetNormal(mesh)
Lpml = 1.0 # width of the PML layer
Lx = 10.0 # width of the interior domain
Ly = 10.0 # heigth of the interior domain
# Attenuation functions
beta_0 = physical_parameters.beta_0 # 280 # propagation
alpha_0 = physical_parameters.alpha_0 # 2.76 # evanescent
# Mesh generation and refinement
nx = 80
ny = 80
mesh = RectangleMesh(Point(- 0.5 * Lx - Lpml, 0.0), Point(0.5 * Lx + Lpml, - Ly - Lpml), nx, ny, "crossed")
# Markers for Dirichlet bc
ff = MeshFunction("size_t", mesh, mesh.geometry().dim() - 1)
Dirichlet().mark(ff, 1)
# Markers for disk source
mf = MeshFunction("size_t", mesh, mesh.geometry().dim())
circle().mark(mf, 1)
# Create function spaces
VE = VectorElement("CG", mesh.ufl_cell(), 1, dim=2)
TE = TensorElement("DG", mesh.ufl_cell(), 0, shape=(2, 2), symmetry=True)
W = FunctionSpace(mesh, MixedElement([VE, TE]))
F = FunctionSpace(mesh, "CG", 2)
V = W.sub(0).collapse()
M = W.sub(1).collapse()
