Numerical study of a nonlinear heat equation for plasma physics

Abstract

This paper is devoted to the numerical approximation of a nonlinear parabolic balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical difficulties, in particular for the long-time behaviour approximation, when solved with standard methods. An efficient numerical scheme is presented in this paper, based on a combination of a directional splitting scheme and the implicit–explicit scheme introduced in Filbet and Jin [A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comput. Phys. 229 (2010), pp. 7625–7648].

Keywords:

• nonlinear heat equation
• IMEX scheme
• finite volume method

2010 AMS Subject Classifications::

• 65M08
• 65M06
• 82D10

Acknowledgements

F. Filbet is partially supported by the European Research Council ERC Starting Grant 2009, project 239983-NuSiKiMo, and C. Negulescu is partially supported by the ANR project ESPOIR.