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An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons

Published online by Cambridge University Press:  03 June 2015

Jessy Mallet ,
Stéphane Brull  and
Bruno Dubroca
Jessy Mallet*
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France Univ. Bordeaux, IMB, UMR 5251, F- 33400 Talence, France
Stéphane Brull*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F- 33400 Talence, France
Bruno Dubroca*
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France Univ. Bordeaux, IMB, UMR 5251, F- 33400 Talence, France
*
Corresponding author.Email:Stephane.Brull@math.u-bordeauxl.fr
Email:mallet@celia.u-bordeauxl.fr
Email:dubroca@celia.u-bordeauxl.fr
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Abstract

In plasma physics domain, the electron transport is described with the Fokker-Planck-Landau equation. The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension. To find a solution compatible with physics conditions, the closure of the moment system is obtained under a minimum entropy principle. This model is proved to satisfy the fundamental properties like a H theorem. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Finally, we validate on numerical test cases the fundamental properties of the full discrete model.

Keywords

35Q8465L0476Y05Entropy minimizationLandau-Fokker-Planck equationmoment systemsentropic scheme
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014 , pp. 422 - 450
Copyright
Copyright © Global Science Press Limited 2014

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