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The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions

dc.relation.isnodouble4c5232b1-11cc-459d-929a-ab85a7d7ca31*
dc.relation.isnodoublefecb656b-49bc-4aad-83b8-f302edb3583c*
hal.structure.identifierInstitut de mécanique des fluides de Toulouse [IMFT]
dc.contributor.authorSARTHOU, Arthur
hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorVINCENT, Stéphane
hal.structure.identifierInstitut de Mathématiques de Marseille [I2M]
dc.contributor.authorANGOT, Philippe
hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorCALTAGIRONE, Jean-Paul
dc.date.accessioned2021-05-14T09:33:41Z
dc.date.available2021-05-14T09:33:41Z
dc.date.issued2020
dc.identifier.issn2165-3852
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/76071
dc.description.abstractEnA new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance , the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.
dc.language.isoen
dc.publisherScientific Research
dc.subject.enFictitious Domain
dc.subject.enImmersed Interface Method
dc.subject.enImmersed Boundary Method
dc.subject.enPenalty Methods
dc.subject.enFinite Volumes
dc.subject.enElliptic Equations
dc.subject.enJump Embedded Conditions
dc.title.enThe Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions
dc.typeArticle de revue
dc.identifier.doi10.4236/ojfd.2020.103015
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halInformatique [cs]/Modélisation et simulation
bordeaux.journalOpen Journal of fluid Dynamics
bordeaux.page239 - 269
bordeaux.volume10
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-02921726
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02921726v1
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