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Kinetic-fluid derivation and mathematical analysis of cross-diffusion-Brinkman system

hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierEcole Supérieure de Technologie d'Essaouira
dc.contributor.authorKARAMI, Fahd
hal.structure.identifierEcole Supérieure de Technologie d'Essaouira
dc.contributor.authorZAGOUR, Mohammed
dc.date.accessioned2024-04-04T03:04:43Z
dc.date.available2024-04-04T03:04:43Z
dc.date.created2019
dc.date.issued2019
dc.identifier.issn0170-4214
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193180
dc.description.abstractEnIn this paper, we propose a new nonlinear model describing dynamical interaction of two species within viscous flow. The proposed model is a cross-diffusion system coupled with Brinkman problem written in terms of velocity fluid, vorticity and pressure, and describing the flow patterns driven by an external source depending on the distribution of species. In the first part, we derive a macroscopic models from the kinetic-fluid equations by using the micro-macro decomposition method. Basing on Schauder fixed-point theory, we prove the existence of weak solutions for the derived model in the second part. The last part is devoted to develop a one dimensional finite volume approximation for the kinetic-fluid model, which are uniformly stable along the transition from kinetic to macroscopic regimes. Our computation method is validated with various numerical tests.
dc.language.isoen
dc.publisherWiley
dc.subject.enFinite volume method
dc.subject.enAsymptotic preserving scheme
dc.subject.enKinetic theory
dc.subject.enCross-diffusion
dc.subject.enBrinkman flows
dc.title.enKinetic-fluid derivation and mathematical analysis of cross-diffusion-Brinkman system
dc.typeArticle de revue
dc.identifier.doi10.1002/mma.5139
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
bordeaux.journalMathematical Methods in the Applied Sciences
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01680584
hal.version1
hal.popularoui
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01680584v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Methods%20in%20the%20Applied%20Sciences&rft.date=2019&rft.eissn=0170-4214&rft.issn=0170-4214&rft.au=BENDAHMANE,%20Mostafa&KARAMI,%20Fahd&ZAGOUR,%20Mohammed&rft.genre=article


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