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I'm trying to solve the heat equation in FiPy and right now it works, but I have one problem:

The material I have to simulate has different diffusion coefficients in the x and y direction (due to its fibre layerd structure). I know, that you can make your diffusion coefficient dependent to a variable in FiPy.

My grid is rectengular, but in the future is has to be able to be unstructured. This would mean, the diffusion coefficient is different for every face.

Has anybody a clue on how to implement this type of dependency?

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The term you're looking for is anisotropic diffusion, which handles differing magnitudes of diffusion based on spatial orientation - usually these are defined using tensors (2x2 for 2D problems and 3x3 for 3D problems). I searched for 'diffusion tensor FiPy' and found a link to their FAQ here:

https://www.ctcms.nist.gov/fipy/documentation/FAQ.html

Hope this helps!

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