Hi all,I would like to calculate a steady state electrical conductivity problem, in a 2D system with position-dependent conductivity tensor. The conductivity tensor has all entries nonzero (even off-diagonal) and is antisymmetric (Hall effect), lacking real principal axes.
As I understand according to the FAQ this should be possible since spatially varying tensor conductivities are supported:
http://www.ctcms.nist.gov/fipy/documentation/FAQ.htmlHowever this still leaves open some questions in practice. I have a few questions which are related to each other:
1. Normally (isotropic case) it is best practice to input the diffusion coefficient as a FaceVariable. For an anisotropic problem, should I still input the rank-2 coefficient as a FaceVariable? I ask because in the FAQ linked above, a CellVariable is used.
2. I want to calculate the flux variable of this problem, which in this case is the electric current. To be precise, I want the flux internally used by FiPy, which in this case should be divergence-free because my PDE has no source terms. The goal is to get the face fluxes and use them to calculate a stream function ( https://en.wikipedia.org/wiki/Stream_function ), which only works for the divergence free case.
Ideally I think this should work, no? numerix.dot(conductivity_tensor, voltage.faceGrad)but it returns a rank-2 object! Even then, if I were to successfully calculate a rank-1 FaceVariable current, I want to be confident that its face-normal current is the true divergence-free current.
3. Can I trust the zero-flux boundary conditions to function in this case?The answers aren't clear since the FiPy documentation doesn't say how tensor diffusions are actually implemented; it only covers the isotropic case. I understand there are some serious subtleties for nonrectangular meshes, and so to make it easy I'm going to stick to a square grid mesh.
Cheers and thanks, -- Mark Lundeberg Postdoctoral researcher, Nano-optoelectronics group ICFO-The Institute of Photonic Sciences http://icfo.eu Mediterranean Technology Park Av. Carl Friedrich Gauss, num. 3 08860 Castelldefels (Barcelona), Spain Telf: +34 93 553 41 65 Fax: +34 93 553 40 00
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