Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

Details Highly anisotropic temperature balance equation and its asymptotic-preserving resolution Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

2012-03-30

arxiv.org/abs/1203.6739v1

Mathematics

Numerical Analysis

Scientific paper

This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge-Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter $0 < \eps <1$, and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.

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