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Equivalent boundary conditions for acoustic media with exponential densities. Application to the atmosphere in helioseismology

hal.structure.identifierAdvanced 3D Numerical Modeling in Geophysics [Magique 3D]
hal.structure.identifierLaboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]
dc.contributor.authorCHABASSIER, Juliette
hal.structure.identifierAdvanced 3D Numerical Modeling in Geophysics [Magique 3D]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDURUFLÉ, Marc
hal.structure.identifierAdvanced 3D Numerical Modeling in Geophysics [Magique 3D]
hal.structure.identifierUniversité de Pau et des Pays de l'Adour [UPPA]
hal.structure.identifierLaboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]
dc.contributor.authorPÉRON, Victor
dc.date.accessioned2024-04-04T02:59:34Z
dc.date.available2024-04-04T02:59:34Z
dc.date.issued2019-11
dc.identifier.issn0096-3003
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192750
dc.description.abstractEnWe present equivalent boundary conditions and asymptotic models for the solution of a transmission problem set in a domain which represents the sun and its atmosphere. This problem models the propagation of an acoustic wave in time-harmonic regime. The specific non-standard feature of this problem lies in the presence of a small parameter δ which represents the inverse rate of the exponential decay of the density in the atmosphere. This problem is well suited for the notion of equivalent conditions and the effect of the atmosphere on the sun is as a first approximation local. This approach leads to solve only equations set in the sun. We derive rigorously equivalent conditions up to the fourth order of approximation with respect to δ for the exact solution u. The construction of equivalent conditions is based on a multiscale expansion in power series of δ for u. Numerical simulations illustrate the theoretical results. Finally we measure the boundary layer phenomenon by introducing a characteristic length that turns out to depend on the mean curvature of the interface between the subdomains.
dc.language.isoen
dc.publisherElsevier
dc.subject.enMultiscale expansions
dc.subject.enBoundary layer
dc.subject.enEquivalent conditions
dc.subject.enHelioseismology
dc.title.enEquivalent boundary conditions for acoustic media with exponential densities. Application to the atmosphere in helioseismology
dc.typeArticle de revue
dc.identifier.doi10.1016/j.amc.2019.04.065
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalApplied Mathematics and Computation
bordeaux.page177-197
bordeaux.volume361
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02320521
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02320521v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Applied%20Mathematics%20and%20Computation&rft.date=2019-11&rft.volume=361&rft.spage=177-197&rft.epage=177-197&rft.eissn=0096-3003&rft.issn=0096-3003&rft.au=CHABASSIER,%20Juliette&DURUFL%C3%89,%20Marc&P%C3%89RON,%20Victor&rft.genre=article


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