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Asymptotic-Preserving Scheme for the M1-Maxwell System in the Quasi-Neutral Regime

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium) Applications to specific types of physical systems Equilibrium statistical mechanics

Published online by Cambridge University Press:  01 February 2016

S. Guisset ,
S. Brull ,
B. Dubroca ,
E. d'Humières ,
S. Karpov  and
I. Potapenko
S. Guisset*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33405 Talence, France Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
S. Brull
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33405 Talence, France
B. Dubroca
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
E. d'Humières
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
S. Karpov
Affiliation:
Keldysh Institute for Applied Mathematics, 125047 Moscow, Russian Federation
I. Potapenko
Affiliation:
Keldysh Institute for Applied Mathematics, 125047 Moscow, Russian Federation
*
*Corresponding author. Email address:guisset@celia.u-bordeaux1.fr (S. Guisset)
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Abstract

This work deals with the numerical resolution of the M1-Maxwell system in the quasi-neutral regime. In this regime the stiffness of the stability constraints of classical schemes causes huge calculation times. That is why we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in different regimes. The first one corresponds to a regime where electromagnetic effects are predominant. The second one on the contrary shows the efficiency of the Asymptotic-Preserving scheme in the quasi-neutral regime. In the latter case the illustrative simulations are compared with kinetic and hydrodynamic numerical results.

Keywords

Asymptotic-Preserving schemeFokker-Planck-Landau equationMaxwell equationsquasi-neutral limitangular M1 moments model

MSC classification

Secondary: 82D10: Plasmas 82B40: Kinetic theory of gases 82C40: Kinetic theory of gases
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 301 - 328
Copyright
Copyright © Global-Science Press 2016 

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