def AdvectionDiffusionGLS(
V: fd.FunctionSpace,
theta: fd.Function,
phi: fd.Function,
PeInv: float = 1e-4,
phi_t: fd.Function = None,
):
PeInv_ct = fd.Constant(PeInv)
rho = fd.TestFunction(V)
F = (inner(theta, grad(phi)) * rho +
PeInv_ct * inner(grad(phi), grad(rho))) * dx
if phi_t:
F += phi_t * rho * dx
h = fd.CellDiameter(V.ufl_domain())
R_U = dot(theta, grad(phi)) - PeInv_ct * div(grad(phi))
if phi_t:
R_U += phi_t
beta_gls = 0.9
tau_gls = beta_gls * ((4.0 * dot(theta, theta) / h**2) + 9.0 *
(4.0 * PeInv_ct / h**2)**2)**(-0.5)
theta_U = dot(theta, grad(rho)) - PeInv_ct * div(grad(rho))
F += tau_gls * inner(R_U, theta_U) * dx()
return F
def __init__(self, V: fd.FunctionSpace, solver_parameters=None) -> None:
"""Reinitialization solver. Returns the level set
to a signed distance function
Args:
V (fd.FunctionSpace): Function space of the level set
"""
self.V = V
self.mesh = V.ufl_domain()
self.DG0 = fd.FunctionSpace(self.mesh, "DG", 0)
self.phi = fd.Function(V)
rho, sigma = fd.TrialFunction(V), fd.TestFunction(V)
a = rho * sigma * dx
self.phi_int = fd.Function(V)
self.A_proj = fd.assemble(a)
self.solver_parameters = {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": "mumps",
}
if solver_parameters:
self.solver_parameters.update(solver_parameters)
