I'm looking into using fipy to solve my system of 3 equations (one Poisson, two continuity), used for semiconductor device simulation (the drift-diffusion system, also known as van Roosbroeck system of equations).
My system is: - singularly perturbed (contains sharp boundary/interface layers) - non-linear. - 2D - time-independent For such a system anisotropic mesh helps a lot with keeping the number of mesh-points small. However classical finite volume scheme (2-point flux approximation, or TPFA) as pointed out in the paper by Droniou [1] puts severe limitations on the kind of mesh you could use. Specifically, you can only use anistropic mesh with quad-tree based mesh (i.e., construction of a axis-aligned quad mesh, followed by splitting each quad into two triangles). If you wish to use an unstructured Delaunay mesh, it has to be isotropic (equilateral triangles) or near-isotropic otherwise the control volume calculation will result in overlaps and the conservation property will be violated (the solution would more likely be incorrect). There are some other aspects of a FV scheme as mentioned in Droniou that I'm still trying to understand (as an engineer, not a mathematician). E.g., monotonicity, coercivity, min-max principle, discrete max principle, etc, etc. So my questions are: - Does fipy handle anisotropic unstructured meshes without any problem? (I'm specifically looking to use bamg for 2D mesh adaptation based on interpolation error reduction/equidistribution) - If not, does fipy provide (or provide a way to implement) MPFA (multi-point flux approximation) or some other non-classical scheme (like HMM) that allows anisotropic unstructured meshes (as discussed in the Drioniou paper [1]) ? - Or, does fipy allow any other way to make vertex-centered control volume calculation that can take into account anisotropy and can make sure there are no control volume overlaps (and as a result, the coefficients stay positive, and monotonicity is maintained, and none of the nice properties are violated) ? Thanks in advance, F [1] J. Droniou, “Finite volume schemes for diffusion equations: Introduction to and review of modern methods,” Math. Models Methods Appl. Sci., vol. 24, no. 08, pp. 1575–1619, Jan. 2014. _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
