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arXiv · 1210.0681

Numerical resolution of an anisotropic non-linear diffusion problem

Stéphane Brull·Fabrice Deluzet·Alexandre Mouton
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Abstract

This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit \varepsilon \infty 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the anisotropy direction and exhibits an accuracy as well as a computational cost independent of the anisotropy strength.

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Stéphane Brull, Fabrice Deluzet, Alexandre Mouton. 2012-10-02. Numerical resolution of an anisotropic non-linear diffusion problem. https://arxiv.org/abs/1210.0681

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