Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations

  • Authors:

  • Andrea Mentrelli;Claudia Negulescu

  • Affiliations:

  • Laboratoire d'Analyse Topologie Probabilités (LATP), Centre de Mathématiques et Informatique (CMI), UMR6632, Université de Provence, Technopôle Chíteau-Gombert, 39, rue F. ...;Laboratoire d'Analyse Topologie Probabilités (LATP), Centre de Mathématiques et Informatique (CMI), UMR6632, Université de Provence, Technopôle Chíteau-Gombert, 39, rue F. ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

Quantified Score

Hi-index 31.45

Visualization

Abstract

Heat transfer in magnetically confined plasmas is a process characterized by non-linear and extremely high anisotropic diffusion phenomena. Standard numerical methods, successfully employed in the numerical treatment of classical diffusion problems, are generally inefficient, or even prone to break down, when such high anisotropies come into play, leading thus to the need of new numerical techniques suitable for this kind of problems. In the present paper, the authors propose a numerical scheme based on an asymptotic-preserving (AP) reformulation of this non-linear evolution problem, generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems [P. Degond, A. Lozinski, J. Narski, C. Negulescu, An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition, J. Comput. Phys. 231 (7) (2012) 2724-2740]. The performances of the here proposed AP scheme are tested numerically; in particular it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy, thus proving to be suitable for the study of anisotropic diffusion in magnetically confined plasmas.