A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LEMOU, Mohammed | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MIEUSSENS, Luc | |
| dc.date.accessioned | 2024-04-04T02:43:20Z | |
| dc.date.available | 2024-04-04T02:43:20Z | |
| dc.date.issued | 2008 | |
| dc.identifier.issn | 1064-8275 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191323 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | transport equations | |
| dc.subject.en | diffusion limit | |
| dc.subject.en | asymptotic preserving schemes | |
| dc.subject.en | stiff terms | |
| dc.title.en | A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/07069479X | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.journal | SIAM Journal on Scientific Computing | |
| bordeaux.page | 334-368 | |
| bordeaux.volume | 31 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00348594 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00348594v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Scientific%20Computing&rft.date=2008&rft.volume=31&rft.issue=1&rft.spage=334-368&rft.epage=334-368&rft.eissn=1064-8275&rft.issn=1064-8275&rft.au=LEMOU,%20Mohammed&MIEUSSENS,%20Luc&rft.genre=article |
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