On the Spitzer-Härm regime and non local approximations: modeling, analysis and numerical simulations

Thierry Goudon 1, 2, 3 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 : This paper is devoted to the derivation of the Spitzer-Härm limit from the coupled system of PDEs describing the evolution of charged particles and electromagnetic fields. We identify a relevant asymptotic regime which leads to a nonlinear diffusion equation for the electron temperature. Then, we discuss some intermediate models, which remain of hydrodynamic nature but involve a nonlocal coupling through integral or pseudodifferential operators. In particular, we exhibit important mathematical properties of the so-called Schurtz-Nicolaï model like the well-posedness and the maximum principle. We also design numerical schemes for the nonlocal models and analyze their consistency and stability properties.
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Submitted on : Monday, November 18, 2013 - 10:18:45 AM
Last modification on : Friday, April 19, 2019 - 2:12:06 PM

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Thierry Goudon, Martin Parisot. On the Spitzer-Härm regime and non local approximations: modeling, analysis and numerical simulations. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2011, 9 (2), pp.568--600. ⟨10.1137/100800269⟩. ⟨hal-00905332⟩

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