Asymptotic Preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction

Abstract

This paper deals with the numerical study of a strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to high anisotropy. Furthermore, the recently proposed Asymptotic-Preserving method (Lozinski et al., 2012) allows one to perform simulations regardless of the anisotropy strength but its application is limited to the case where the anisotropy direction is given by a field whose lines are all open. In this paper we introduce a new Asymptotic-Preserving method, which overcomes those limitations without any loss of precision or increase in computational costs. The convergence of the method is shown to be independent of the anisotropy parameter 0<ε<1 for fixed coarse Cartesian grids, and for variable anisotropy directions. The context of this work is magnetically confined fusion plasmas.