Setting diffusion coefficient using GMSH face definition

[Noxical]

I want to set the diffusion coefficient / thermal conductivity in a wall based on the specific wall material isolation property.

I cant figure out how to do this using GMSH. My code is attached below. It works only by setting the D value using the X, Y faceCenters. However, I would prefer to use GMSH to specifiy the correct material within the line loop.

from fipy import *
import numpy as np

mesh = Gmsh2D('''
SetFactory("OpenCASCADE");

ns = 0.01;

x0 = 0;
x1 = 1;
x2 = 0.9;

x3 = 0.8;
x4 = 0.7;

y0 = 0;
y1 = 1;
y2 = 0.1;

y3 = 0.2;
y4 = 0.3;

Point(1) = {x0, y0, 0, ns};
Point(2) = {x1, y0, 0, ns};
Point(3) = {x1, y1, 0, ns};
Point(4) = {x2, y1, 0, ns};
Point(5) = {x2, y2, 0, ns};
Point(6) = {x0, y2, 0, ns};

Point(8) = {x3, y1, 0, ns};
Point(9) = {x3, y3, 0, ns};
Point(10) = {x0, y3, 0, ns};

Point(11) = {x4, y1, 0, ns};
Point(12) = {x4, y4, 0, ns};
Point(13) = {x0, y4, 0, ns};

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(7) = {4, 8};
Line(8) = {8, 9};
Line(9) = {9, 10};
Line(10) = {10, 6};

Line(11) = {8, 11};
Line(12) = {11, 12};
Line(13) = {12, 13};
Line(14) = {13, 10};

Line Loop(1) = {1,2,3,7,11,12,13,14,10,6};
Plane Surface(1) = {1};
Physical Surface("wall") = {1};

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

Physical Line("outer") = {1,2};
Physical Line("inner") = {12,13};

'''% locals())

X,Y = mesh.faceCenters
T = CellVariable(name="isotherm", mesh=mesh, value=1.)

D=FaceVariable(mesh=mesh, value=1.)

mask = mesh.physicalFaces["shell"]

D.setValue(0.1, where=mask) # this doesn work

D.setValue(1, where= (X>0.9) + (Y<0.1))
D.setValue(2, where= (X<0.9) + (Y>0.1))

T.constrain(1400, mesh.physicalFaces['inner'] )
T.constrain(40, mesh.physicalFaces['outer'] )

eq = TransientTerm(var=T) == DiffusionTerm(D, var=T)

steps = 2 #time steps
dt = 600

for i in range(steps):

eq.solve(var=T, dt=dt)

vi = Viewer(T)

[guyer]

Please see the use of Physical Surface in the documentation for Gmsh2D

[Noxical]

I have looked at the documentation, but this only mentions the ability to change the cellVariables using gmsh physical surface definition, this works.
However there is no clear example of how to do this to the diffusion coefficients, which are faceVariables. I would expect i will work the same, but it doens't seem to be straight forward.

[guyer]

Gmsh defines elements and does not provide any ready mechanism to label the internal faces within a domain.

The simplest thing is to define your diffusion coefficient as a CellVariable and let FiPy interpolate it. By default, it will calculate the arithmetic mean at the faces, e.g.,

D=CellVariable(mesh=mesh)
D.setValue(1., where=mesh. physicalCells["zone1"])
D.setValue(2., where=mesh. physicalCells["zone1"])
eq = TransientTerm(var=T) == DiffusionTerm(D, var=T)

is completely equivalent to

eq = TransientTerm(var=T) == DiffusionTerm(D.arithmeticFaceValue, var=T)

You could specify a different interpolation scheme, if you wished:

eq = TransientTerm(var=T) == DiffusionTerm(D.harmonicFaceValue, var=T)

A more physically valid thing to do for diffusion coefficients might be

Ea = CellVariable(mesh=mesh)
Ea.setValue(Ea1, where=mesh. physicalCells["zone1"])
Ea.setValue(Ea2, where=mesh. physicalCells["zone2"])
D = D0 * numerix.exp(-(Ea / (k * T)).arithmeticFaceValue))
eq = TransientTerm(var=T) == DiffusionTerm(D, var=T)

[Noxical]

Thanks. This solves the problem.