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Solution Property Preserving Reconstruction for Finite Volume Scheme: a BVD+MOOD framework

dc.contributor.authorTANN, Siengdy
hal.structure.identifierLaboratoire de Mécanique, Modélisation et Procédés Propres [M2P2]
dc.contributor.authorDENG, Xi
dc.contributor.authorSHIMIZU, Yuya
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLOUBÈRE, Raphaël
hal.structure.identifierTokyo Institute of Technology [Tokyo] [TITECH]
dc.contributor.authorXIAO, Feng
dc.date2019-12
dc.date.accessioned2024-04-04T02:58:36Z
dc.date.available2024-04-04T02:58:36Z
dc.date.issued2019-12
dc.identifier.issn0271-2091
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192673
dc.description.abstractEnThe purpose of this work is to build a general framework to reconstruct the underlying fields within a Finite Volume (FV) scheme solving a hyperbolic system of PDEs (Partial Differential Equations). In an FV context, the data are piece-wise constants per computational cell and the physical fields are reconstructed taking into account neighbor cell values. These reconstructions are further used to evaluate the physical states usually used to feed a Riemann solver which computes the associated numerical fluxes. The physical field reconstructions must obey some properties linked to the system of PDEs such as the positivity, but also some numerically based ones, like an essentially non-oscillatory behaviour. Moreover, the reconstructions should be high accurate for smooth flows and robust/stable for discontinuous solutions. To ensure a Solution Property Preserving Reconstruction, we introduce a methodology to blend high/low order polynomials and hyperbolic tangent reconstructions. A Boundary Variation Diminishing (BVD) algorithm is employed to select the best reconstruction in each cell. An a posteriori MOOD detection procedure is employed to ensure the positivity by re-computing the rare problematic cells using a robust first-order FV scheme. We illustrate the performance of the proposed scheme via the numerical simulations for some benchmark tests which involve vacuum or near vacuum states, strong discontinuities and also smooth flows. The proposed scheme maintains high accuracy on smooth profile, preserves the positivity and can eliminate the oscillations in the vicinity of discontinuities while maintaining sharper discontinuity with superior solution quality compared to classical high accurate FV schemes.
dc.language.isoen
dc.publisherWiley
dc.subject.enTHINC
dc.subject.enmulti-stage-BVD
dc.subject.enFinite volume
dc.subject.enpositivity-preserving
dc.subject.enhyperbolic system of PDEs
dc.subject.enMOOD
dc.title.enSolution Property Preserving Reconstruction for Finite Volume Scheme: a BVD+MOOD framework
dc.typeArticle de revue
dc.identifier.doi10.1002/fld.4798
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalInternational Journal for Numerical Methods in Fluids
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02397156
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02397156v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International%20Journal%20for%20Numerical%20Methods%20in%20Fluids&rft.date=2019-12&rft.eissn=0271-2091&rft.issn=0271-2091&rft.au=TANN,%20Siengdy&DENG,%20Xi&SHIMIZU,%20Yuya&LOUB%C3%88RE,%20Rapha%C3%ABl&XIAO,%20Feng&rft.genre=article


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