Titre :

Asymptotic-preserving projective integration schemes for kinetic equations in the diffusion limit

Auteur(s) :

Lafitte, Pauline [Auteur]
Mathématiques Appliquées aux Systèmes - EA 4037 [MAS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Samaey, Giovanni [Auteur]
Université Catholique de Louvain = Catholic University of Louvain [UCL]

Titre de la revue :

SIAM Journal on Scientific Computing

Pagination :

A579-A602

Éditeur :

Society for Industrial and Applied Mathematics

Date de publication :

2012

ISSN :

1064-8275

Mot(s)-clé(s) en anglais :

kinetic equation
diffusion
projective integration

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps ...
Lire la suite >We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on the diffusion time scale. We show that, with an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the diffusion equation, whereas the required number of inner steps does not depend on the mean free path. We also provide a consistency result. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the diffusion equation in the limit of vanishing mean free path. The analysis is illustrated with numerical results, and we present an application to the Su-Olson test.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL