def get_laplace(q, phi):
h = fd.avg(fd.CellVolume(mesh)) / fd.FacetArea(mesh)
mu = eta / h
n = fd.FacetNormal(mesh)
ad = (-fd.inner(2 * fd.avg(phi * n), fd.avg(fd.grad(q))) -
fd.inner(fd.avg(fd.grad(phi)), 2 * fd.avg(q * n)) + mu *
fd.inner(2 * fd.avg(phi * n), 2 * fd.avg(q * n))) * fd.dS
ad += fd.inner(fd.grad(q), fd.grad(phi)) * fd.dx
return ad
def min_mesh_size(mesh):
"""Calculate minimum cell diameter in mesh
Args:
mesh ([type]): [description]
Returns:
float: [description]
"""
DG0 = fd.FunctionSpace(mesh, "DG", 0)
h_sizes = fd.assemble(
fd.CellDiameter(mesh) / fd.CellVolume(mesh) * fd.TestFunction(DG0) *
fd.dx).dat.data_ro
local_min_size = np.max(h_sizes)
min_size = mesh.comm.allreduce(local_min_size, op=MPI.MAX)
return min_size
wh, vh, mu_h = fd.TestFunctions(W) # 3.2) Set initial conditions # ---- previous solution # concentrations c0 = fd.Function(DG1, name="c0") c0.assign(0.0) # ---------------------- # 3.4) Variational Form # ---------------------- # coefficients dt = np.sqrt(tol) dtc = fd.Constant(dt) n = fd.FacetNormal(mesh) h = fd.sqrt(2) * fd.CellVolume(mesh) / fd.CellDiameter(mesh) # advective velocity velocity = fd.Function(vDG1) velocity.interpolate(v_inlet) vnorm = fd.sqrt(fd.dot(velocity, velocity)) # upwind term vn = 0.5 * (fd.dot(velocity, n) + abs(fd.dot(velocity, n))) cupw = fd.conditional(fd.dot(velocity, n) > 0, ch, lmbd_h) # Diffusion tensor Diff = fd.Identity(mesh.geometric_dimension()) * Dm # Diff = fd.Identity(mesh.geometric_dimension())*(Dm + d_t*vnorm) + \ # fd.Constant(d_l-d_t)*fd.outer(velocity, velocity)/vnorm