581 articles – 596 Notices  [english version]
 HAL : hal-00533327, version 1
 Kinetic and related models 4, 2 (2011) 441-477
 An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits.
 Nicolas Crouseilles 1, 2, Mohammed Lemou 3
 (2011)
 In this work, we extend the micro-macro decomposition based numerical schemes developed in \cite{benoune} to the collisional Vlasov-Poisson model in the diffusion and high-field asymptotics. In doing so, we first write the Vlasov-Poisson model as a system that couples the macroscopic (equilibrium) part with the remainder part. A suitable discretization of this micro-macro model enables to derive an asymptotic preserving scheme in the diffusion and high-field asymptotics. In addition, two main improvements are presented: On the one hand a self-consistent electric field is introduced, which induces a specific discretization in the velocity direction, and represents a wide range of applications in plasma physics. On the other hand, as suggested in \cite{noteL}, we introduce a suitable reformulation of the micro-macro scheme which leads to an asymptotic preserving property with the following property: It degenerates into an implicit scheme for the diffusion limit model when $\varepsilon\rightarrow 0$, which makes it free from the usual diffusion constraint $\Delta t={\cal O}(\Delta x^2)$ in all regimes. Numerical examples are used to demonstrate the efficiency and the applicability of the schemes for both regimes.
 1 : Institut de Recherche Mathématique Avancée (IRMA) CNRS : UMR7501 – Université de Strasbourg 2 : CALVI (INRIA Nancy - Grand Est / IECN / LSIIT / IRMA) CNRS : UMR7005 – INRIA – Université de Strasbourg – Université de Lorraine 3 : Institut de Recherche Mathématique de Rennes (IRMAR) CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
 Domaine : Mathématiques/Analyse numérique
Liste des fichiers attachés à ce document :
 PDF
 dec-MM.pdf(665.6 KB)
 hal-00533327, version 1 http://hal.archives-ouvertes.fr/hal-00533327 oai:hal.archives-ouvertes.fr:hal-00533327 Contributeur : Nicolas Crouseilles <> Soumis le : Vendredi 5 Novembre 2010, 16:52:17 Dernière modification le : Jeudi 25 Août 2011, 14:23:51