Volume 15, Issue 2
An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons

Jessy Mallet, Stéphane Brull & Bruno Dubroca

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

Published online: 2014-02

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  • Abstract

In plasma physics domain, the electron transport is described with the FokkerPlanck-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.

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@Article{CiCP-15-422, author = {}, title = {An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {2}, pages = {422--450}, abstract = {

In plasma physics domain, the electron transport is described with the FokkerPlanck-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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050612.030513a}, url = {http://global-sci.org/intro/article_detail/cicp/7100.html} }
TY - JOUR T1 - An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons JO - Communications in Computational Physics VL - 2 SP - 422 EP - 450 PY - 2014 DA - 2014/02 SN - 15 DO - http://dor.org/10.4208/cicp.050612.030513a UR - https://global-sci.org/intro/article_detail/cicp/7100.html KW - AB -

In plasma physics domain, the electron transport is described with the FokkerPlanck-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.

Jessy Mallet, Stéphane Brull & Bruno Dubroca. (2020). An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons. Communications in Computational Physics. 15 (2). 422-450. doi:10.4208/cicp.050612.030513a
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