WENO schemes applied to the quasi-relativistic Vlasov–Maxwell model for laser–plasma interaction

Francesco Vecil; Pep Mulet Mestre; Simon Labrunie

doi:10.1016/j.crme.2014.06.009

Theoretical and numerical approaches for Vlasov–Maxwell equations

WENO schemes applied to the quasi-relativistic Vlasov–Maxwell model for laser–plasma interaction
[Schémas WENO appliqués au modèle Vlasov–Maxwell quasi-relativiste pour l'interaction laser–plasma]

Francesco Vecil ¹ ; Pep Mulet Mestre ² ; Simon Labrunie ^3,⁴

¹ Laboratoire de mathématiques, Université Blaise-Pascal (Clermont-Ferrand 2), UMR 6620, CNRS, campus des Cézeaux, BP 80026, 63171 Aubière, France
² Universitat de València, Departament de Matemàtica Aplicada, calle del Doctor Moliner 50, Burjassot 46100, Spain
³ Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, 54506 Vandœuvre-lès-Nancy, France
⁴ CNRS, Institut Élie Cartan de Lorraine, UMR 7502, 54506 Vandœuvre-lès-Nancy, France

Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 583-594.

Résumé
Abstract

Dans cet article, nous nous intéressons aux méthodes de type WENO pour la simulation du modèle Vlasov–Maxwell quasi-relativiste (QRVM) 1D, utilisé pour décrire la façon dont une onde laser interagit avec un plasma et le réchauffe en le pénétrant. Nous proposons plusieurs méthodes non oscillatoires fondées sur des discrétisations en temps, soit Runge–Kutta (explicites) soit Time-Splitting (implicites). Ensuite, nous présentons des expériences numériques préliminaires.

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.

Reçu le : 2014-05-15
Accepté le : 2014-06-10
Publié le : 2014-08-06

DOI : 10.1016/j.crme.2014.06.009

Keywords: Vlasov–Maxwell, WENO, Laser–plasma interaction, Runge–Kutta schemes, Strang splitting
Mot clés : Vlasov–Maxwell, WENO, Interaction laser–plasma, Schémas de Runge–Kutta, Splitting de Strang

Affiliations des auteurs :

Francesco Vecil ¹ ; Pep Mulet Mestre ² ; Simon Labrunie ^{3, 4}

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     author = {Francesco Vecil and Pep Mulet Mestre and Simon Labrunie},
     title = {WENO schemes applied to the quasi-relativistic {Vlasov{\textendash}Maxwell} model for laser{\textendash}plasma interaction},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {583--594},
     publisher = {Elsevier},
     volume = {342},
     number = {10-11},
     year = {2014},
     doi = {10.1016/j.crme.2014.06.009},
     language = {en},
}

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%A Pep Mulet Mestre
%A Simon Labrunie
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Francesco Vecil; Pep Mulet Mestre; Simon Labrunie. WENO schemes applied to the quasi-relativistic Vlasov–Maxwell model for laser–plasma interaction. Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 583-594. doi : 10.1016/j.crme.2014.06.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.009/

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