Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

Alexei Lozinski; Jacek Narski; Claudia Negulescu

Highly anisotropic temperature balance equation and its asymptotic-preserving resolution

Numerical Analysis 2012-04-02 v1

Authors: Alexei Lozinski , Jacek Narski , Claudia Negulescu

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.

Keywords

anisotropic heat equation asymptotic-preserving method Runge-Kutta scheme numerical convergence fusion plasmas

Cite

@article{arxiv.1203.6739,
  title  = {Highly anisotropic temperature balance equation and its asymptotic-preserving resolution},
  author = {Alexei Lozinski and Jacek Narski and Claudia Negulescu},
  journal= {arXiv preprint arXiv:1203.6739},
  year   = {2012}
}

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