| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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Mathématiques/Analyse numérique
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| Titre : |
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A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit |
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| Auteur(s) : |
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Mohammed Lemou 1, Luc Mieussens ( ) 2 |
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| Laboratoire : |
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| Résumé : |
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We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts. We also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part. By using a suitable time semi-implicit discretization, our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes. It is asymptotic preserving in the following sense: when the mean free path of the particles is small, our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model. A uniform stability property is proved for the simple telegraph model. Various boundary conditions are studied. Our method is validated in one-dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes. |
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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| SIAM Journal on Scientific Computing (J. Sci. Comput.) |
| Publisher |
Society for Industrial and Applied Mathematics |
| ISSN |
1064-8275 |
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| Audience : |
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internationale |
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| Date de publication : |
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2008 |
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| Volume : |
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31 |
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| Numéro : |
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1 |
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| Page, identifiant, ... : |
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334-368 |
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| Mots Clés : |
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transport equations – diffusion limit – asymptotic preserving schemes – stiff terms |
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