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hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorLEMOU, Mohammed
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMIEUSSENS, Luc
dc.date.accessioned2024-04-04T02:43:20Z
dc.date.available2024-04-04T02:43:20Z
dc.date.issued2008
dc.identifier.issn1064-8275
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191323
dc.description.abstractEnWe 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.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.entransport equations
dc.subject.endiffusion limit
dc.subject.enasymptotic preserving schemes
dc.subject.enstiff terms
dc.title.enA new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit
dc.typeArticle de revue
dc.identifier.doi10.1137/07069479X
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalSIAM Journal on Scientific Computing
bordeaux.page334-368
bordeaux.volume31
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00348594
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00348594v1
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