Non―local macroscopic models based on Gaussian closures for the Spitzer―Härm regime

Thierry Goudon 1, 2 Martin Parisot 3
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : The Spitzer-Härm regime arising in plasma physics leads asymptotically to a nonlinear diffusion equation for the electron temperature. In this work we propose a hierarchy of models intended to retain more features of the underlying modeling based on kinetic equations. These models are of non--local type. Nevertheless, owing to energy discretization they can lead to coupled systems of diffusion equations. We make the connection between the different models precise and bring out some mathematical properties of the models. A numerical scheme is designed for the approximate models, and simulations validate the proposed approach.
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Submitted on : Monday, November 18, 2013 - 10:18:49 AM
Last modification on : Tuesday, July 3, 2018 - 11:42:58 AM

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Thierry Goudon, Martin Parisot. Non―local macroscopic models based on Gaussian closures for the Spitzer―Härm regime. Kinetic and Related Models , AIMS, 2011, 4 (3), pp.735--766. ⟨10.3934/krm.2011.4.735⟩. ⟨hal-00905335⟩

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