Asymptotic-preserving projective integration ...
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Article dans une revue scientifique: Article original
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Title :
Asymptotic-preserving projective integration schemes for kinetic equations in the diffusion limit
Author(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]
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]
Journal title :
SIAM Journal on Scientific Computing
Pages :
A579-A602
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2012
ISSN :
1064-8275
English keyword(s) :
kinetic equation
diffusion
projective integration
diffusion
projective integration
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Source :
Submission date :
2025-01-24T11:15:21Z
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