An entropic scheme for an angular moment model for the classical Fokker-Planck-Landau equation of electrons

Jessy Mallet (1, 2) , Stéphane Brull (2) , Bruno Dubroca (1, 2)

1 CELIA - Centre d'Etudes Lasers Intenses et Applications
2 IMB - Institut de Mathématiques de Bordeaux

In plasma physics domain, the electron transport is describedwith 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.

Mots clés: entropy minimization; Landau-Fokker-Planck equation; moment systems; entropic scheme.; entropic scheme

Domaines: Equations aux dérivées partielles [math.AP]

Jessy Mallet, Stéphane Brull, Bruno Dubroca. An entropic scheme for an angular moment model for the classical Fokker-Planck-Landau equation of electrons. Communications in Computational Physics, 2014, 15, pp.422-450. ⟨hal-00960296⟩