Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time

Jacek Narski (1) , Alexei Lozinski (2) , Claudia Negulescu (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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 < epsilon < 1, and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.

Domaines: Analyse numérique [math.NA]

Jacek Narski, Alexei Lozinski, Claudia Negulescu. Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time. ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (6), pp.1701 - 1724. ⟨10.1051/m2an/2014016⟩. ⟨hal-01881558⟩