Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

Abstract

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.

References in corpus (1)

• An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition

Cited by in corpus (5)

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• An Asymptotic Preserving method for strongly anisotropic diffusion equations based on field line integration
• Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modelling
• Uniform convergent scheme for strongly anisotropic diffusion equations with closed field lines