High order asymptotic-preserving schemes for the Boltzmann equation

Giacomo Dimarco; Lorenzo Pareschi

doi:10.1016/j.crma.2012.05.010

Partial Differential Equations/Numerical Analysis

High order asymptotic-preserving schemes for the Boltzmann equation
[Schémas dʼordre élévé et préservant lʼasymptotique pour lʼéquation de Boltzmann]

Présenté par : Olivier Pironneau

Giacomo Dimarco ¹ ; Lorenzo Pareschi ²

¹ Université de Toulouse, UPS, INSA, UT1, UTM, CNRS, UMR 5219, institut de mathématiques de Toulouse, 31062 Toulouse, France
² Mathematics Department, University of Ferrara and CMCS, Ferrara, Italy

Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 481-486.

Résumé
Abstract

Dans cette Note nous discutons la construction de schémas dʼordre élevé pour lʼéquation de Boltzmann qui préservent la limite asymptotique. Les méthodes sont basées sur lʼutilisation de schémas de Runge–Kutta explicites–implicites combinées avec une technique de pénalisation introduit récemment par Filbet et Jin (2010) [6].

In this Note we discuss the construction of high order asymptotic preserving numerical schemes for the Boltzmann equation. The methods are based on the use of Implicit–Explicit (IMEX) Runge–Kutta methods combined with a penalization technique recently introduced in Filbet and Jin (2010) [6].

Reçu le : 2012-01-31
Accepté le : 2012-05-22
Publié le : 2012-05-01

DOI : 10.1016/j.crma.2012.05.010

Affiliations des auteurs :

Giacomo Dimarco ¹ ; Lorenzo Pareschi ²

¹ Université de Toulouse, UPS, INSA, UT1, UTM, CNRS, UMR 5219, institut de mathématiques de Toulouse, 31062 Toulouse, France
² Mathematics Department, University of Ferrara and CMCS, Ferrara, Italy

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     author = {Giacomo Dimarco and Lorenzo Pareschi},
     title = {High order asymptotic-preserving schemes for the {Boltzmann} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {481--486},
     publisher = {Elsevier},
     volume = {350},
     number = {9-10},
     year = {2012},
     doi = {10.1016/j.crma.2012.05.010},
     language = {en},
}

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Giacomo Dimarco; Lorenzo Pareschi. High order asymptotic-preserving schemes for the Boltzmann equation. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 481-486. doi : 10.1016/j.crma.2012.05.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.010/

Bibliographie
Cité par

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