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A Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems

hal.structure.identifierLaboratoire d'Analyse, Topologie, Probabilités [LATP]
dc.contributor.authorANGOT, Philippe
hal.structure.identifierTransferts, écoulements, fluides, énergétique [TREFLE]
dc.contributor.authorCALTAGIRONE, Jean-Paul
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorFABRIE, Pierre
dc.contributor.editorJ. Fořt et al. (Eds)
dc.date.accessioned2024-04-04T02:26:52Z
dc.date.available2024-04-04T02:26:52Z
dc.date.created2011-03-07
dc.date.issued2011-06
dc.date.conference2011-06-06
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189988
dc.description.abstractEnWe present a new fast vector penalty-projection method (VPP$_{\eps}$), issued from noticeable improvements of previous works [7, 3, 4], to efficiently compute the solution of unsteady Navier-Stokes/Brinkman problems governing incompressible multiphase viscous flows. The method is also efficient to solve anisotropic Darcy problems. The key idea of the method is to compute at each time step an accurate and curl-free approximation of the pressure gradient increment in time. This method performs a two-step approximate divergence-free vector projection yielding a velocity divergence vanishing as $\mathcal{O}(\eps\, \dt)$, $\dt$ being the time step, with a penalty parameter $\eps$ as small as desired until the machine precision, e.g. $\eps= 10^{−14}$, whereas the solution algorithm can be extremely fast and cheap. The method is numerically validated on a benchmark problem for two-phase bubble dynamics where we compare it to the Uzawa augmented Lagrangian (UAL) and scalar incremental projection (SIP) methods. Moreover, a new test case for fluid-structure interaction problems is also investigated. That results in a robust method running faster than usual methods and being able to efficiently compute accurate solutions to sharp test cases whatever the density, viscosity or anisotropic permeability jumps, whereas other methods crash.
dc.language.isoen
dc.publisherSpringer-Verlag (Berlin)
dc.source.titleFinite Volumes for Complex Applications VI - Problems & Perspectives
dc.subject.enVector penalty-projection
dc.subject.enPenalty method
dc.subject.enSplitting method
dc.subject.enMultiphase Navier-Stokes/Brinkman
dc.subject.enAnisotropic Darcy problem
dc.subject.enIncompressible flows
dc.title.enA Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems
dc.typeCommunication dans un congrès
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.page39-47
bordeaux.volume4
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleInternational Symposium FVCA6
bordeaux.countryCZ
bordeaux.title.proceedingFinite Volumes for Complex Applications VI - Problems & Perspectives
bordeaux.conference.cityPrague
bordeaux.peerReviewedoui
hal.identifierhal-00610690
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2011-06-10
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00610690v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Finite%20Volumes%20for%20Complex%20Applications%20VI%20-%20Problems%20&%20Perspectives&rft.date=2011-06&rft.volume=4&rft.issue=1&rft.spage=39-47&rft.epage=39-47&rft.au=ANGOT,%20Philippe&CALTAGIRONE,%20Jean-Paul&FABRIE,%20Pierre&rft.genre=unknown


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