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Journal Articles Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Year : 2011

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

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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Dates and versions

hal-00905332 , version 1 (18-11-2013)

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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, 2011, 9 (2), pp.568--600. ⟨10.1137/100800269⟩. ⟨hal-00905332⟩
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