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kynan/cahn_hilliard.py

Created October 1, 2015 20:11
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Cahn-HIlliard Firedrake code for DSI screen
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cahn_hilliard.py
from firedrake import *
mesh = UnitSquareMesh(100, 100)
V = FunctionSpace(mesh, "CG", 1)
W = V*V
gamma = Constant(0.005)
D = Constant(10)
q, v = TestFunctions(W)
u = Function(W)
u0 = Function(W)
phi, mu = split(u)
phi0, mu0 = split(u0)
phi = variable(phi)
f = 10*(phi**2 - 1)**2
dfdphi = diff(f, phi)
theta = 0.5
mu_theta = (1-theta)*mu0 + theta*mu
dt = 5e-6
F = ((phi - phi0)*q + dt*D*dot(grad(mu_theta), grad(q)) +
(mu - dfdphi)*v - gamma*dot(grad(phi), grad(v)))*dx
for _ in range(200):
u0.assign(u)
solve(F == 0, u)
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