Get FaceVariable at GMSH Physical Line

Question

I successfully set up a very simple diffusion problem including a source face (continuum) and sink faces (sidewall, top) on a mesh generated with GMSH.

from fipy import *

mesh = Gmsh2D('''Point(1) = {0, 0, 0, 1.0};
Point(2) = {12, 0, 0, 0.1};
Point(3) = {12, 16, 0, 0.1};
Point(4) = {15, 16, 0, 0.1};
Point(5) = {15, 100, 0, 1.0};
Point(6) = {0, 100, 0, 1.0};

Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 5};
Line(5) = {5, 6};
Line(6) = {6, 1};

Line Loop(1) = {1, 2, 3, 4, 5, 6};

Plane Surface(1) = {1};

Physical Line("continuum") = {5};
Physical Line("sidewall") = {2};
Physical Line("top") = {3};

Physical Surface("domain") = {1};
''')

c = CellVariable(name='concentration', mesh=mesh, value=0.)

c.faceGrad.constrain([-0.05 * c.harmonicFaceValue], mesh.physicalFaces["sidewall"])
c.faceGrad.constrain([0.05 * c.harmonicFaceValue], mesh.physicalFaces["top"])
c.constrain(1., mesh.physicalFaces["continuum"])

dim = 1.
D = 1.
dt = 50 * dim**2 / (2 * D)
steps = 100

eq = TransientTerm() == DiffusionTerm(coeff=D)

viewer = Viewer(vars=(c, c.grad), datamin=0., datamax=1.)

for step in range(steps):
    eq.solve(var=c, dt=dt)
    viewer.plot()

TSVViewer(vars=(c, c.grad)).plot(filename="conc.tsv")

raw_input('Press any key...')

The calculation works as intended, however I would like to access the gradient at the physical faces I set up in GMSH. I know that I can get the gradient at faces using c.faceGrad and the mask representing the physical faces using mesh.physicalFaces['sidewall']. To get the gradient at the faces contained in the physical face, I would expect to use indexing like c.faceGrad[mesh.physicalFaces['sidewall']]. However, this does not yield the desired result. Is there a way to access the FaceVariable at locations specified by physicalFaces?

Answer 1

Remember that c.faceGrad has shape (2, 22009) so the mask operates on the second index as the shape of mesh.physicalFaces['sidewall'] is (22009,). So, try

c.faceGrad[:, mesh.physicalFaces['sidewall']]

and to access the correct shape use

np.array(c.faceGrad[:, mesh.physicalFaces['sidewall']]).shape

which is (2, 160).