Dear FiPy developers,
I am trying to solve a diffusion PDE with a non-linear diffusion term in a
domain that contains 2 subdomains. Those subdomains are not specified in the
mesh, i.e., the mesh treats everything as a single domain. I want to achieve
diffusivity = 0 between the faces of one of the subdomains. In other words, I
am trying to mask the diffusivity FaceVariable so that some faces (given, for
instance, by the values of a fp.FaceVariable) are identically 0.
My approach so far is the following:
eq = fp.TransientTerm() == fp.DiffusionTerm(coeff=compute_diffusivity(phi))
And compute_diffusivity is given by:
def compute_diffusivity(phi):
diff = fp.numerix.sqrt(2.0*phi) / fp.numerix.exp(4.0*phi**2)
diff_face = fp.FaceVariable(mesh=mesh, value=diff.arithmeticFaceValue.value)
# Create mask of subdomain, all ones except zeros where needed
mask_face = fp.FaceVariable(...)
# Apply mask to diffusivity and return.
# Multiplication works because the target value at the mask is zero.
return fp.FaceVariable(mesh=mesh, value=diff_face.value * mask_face.value)
FiPy does solve the problem, but I am worried that it does not understand that
the diffusion variable is non-linear. I suspect that the problem is that the
.value method used to construct the FaceVariable is determining its value
directly, without the lazy evaluation of phi.
How can I solve this problem? What is the best way to set such a mask in FiPy?
Another approach might be to define the subdomains within the mesh (using Gmsh
'physical groups', perhaps?) and then reading and using it in FiPy. However, I
don't know how to do either of those things. (Extra info: I need my code to be
useful both with meshes created within FiPy and by Gmsh).
I would really appreciate your help. Thank you in advance!
Iñaki
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