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An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorBENNOUNE, Mounir
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.accessioned2024-04-04T02:39:53Z
dc.date.available2024-04-04T02:39:53Z
dc.date.created2009-03-09
dc.date.issued2009
dc.identifier.issn0935-1175
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191016
dc.description.abstractEnIn this paper we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. This scheme is uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the Kac model that couples a kinetic equation with macroscopic ones. This method is validated with various test cases and compared to other standard methods.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enkinetic-equations
dc.subject.ennumerical schemes
dc.subject.enrelaxation schemes
dc.subject.engas
dc.title.enAn asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit
dc.typeArticle de revue
dc.identifier.doi10.1007/s00161-009-0116-2
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalContinuum Mechanics and Thermodynamics
bordeaux.page401-421
bordeaux.volume21
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00383271
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00383271v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Continuum%20Mechanics%20and%20Thermodynamics&rft.date=2009&rft.volume=21&rft.issue=5&rft.spage=401-421&rft.epage=401-421&rft.eissn=0935-1175&rft.issn=0935-1175&rft.au=BENNOUNE,%20Mounir&LEMOU,%20Mohammed&MIEUSSENS,%20Luc&rft.genre=article


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