Commun. Comput. Phys., 15 (2014), pp. 422-450.


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

Jessy Mallet 1*, Stephane Brull 2, Bruno Dubroca 1

1 Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France; Univ. Bordeaux, IMB, UMR 5251, F- 33400 Talence, France.
2 Univ. Bordeaux, IMB, UMR 5251, F- 33400 Talence, France.

Received 5 June 2012; Accepted (in revised version) 3 May 2013
Available online 10 September 2013
doi:10.4208/cicp.050612.030513a

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.

AMS subject classifications: 35Q84, 65L04, 76Y05

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Key words: Entropy minimization, Landau-Fokker-Planck equation, moment systems, entropic scheme.

*Corresponding author.
Email: Stephane.Brull@math.u-bordeaux1.fr (S. Brull), mallet@celia.u-bordeaux1.fr (J. Mallet), dubroca@celia.u-bordeaux1.fr (B. Dubroca)
 

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