| Issue |
ESAIM: M2AN
Volume 48, Number 6, November-December 2014
|
|
|---|---|---|
| Page(s) | 1701 - 1724 | |
| DOI | https://doi.org/10.1051/m2an/2014016 | |
| Published online | 26 September 2014 | |
Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time ∗
1 Université de Toulouse, UPS, INSA,
UT1, UTM, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062
Toulouse,
France.
jacek.narski@math.univ-toulouse.fr;
claudia.negulescu@math.univ-toulouse.fr
2 Laboratoire de Mathematiques CNRS UMR
6623, Université de Franche-Comté, 16 route de Gray, 25030
Besançon cedex,
France.
alexei.lozinski@univ-fcomte.fr
Received:
20
April
2012
Revised:
14
February
2014
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 , and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.
Mathematics Subject Classification: 65N30 / 65Z05 / 35K20
Key words: Anisotropic parabolic equation / Ill-conditioned problem / singular perturbation model / limit model / asymptotic preserving scheme
© EDP Sciences, SMAI, 2014
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