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An arbitrary high order and positivity preserving method for the shallow water equations

hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorCIALLELLA, M.
hal.structure.identifierUniversität Zürich [Zürich] = University of Zurich [UZH]
dc.contributor.authorMICALIZZI, Lorenzo
hal.structure.identifierJohannes Gutenberg - Universität Mainz = Johannes Gutenberg University [JGU]
dc.contributor.authorÖFFNER, Philipp
hal.structure.identifierSISSA MathLab [Trieste]
dc.contributor.authorTORLO, Davide
dc.date.accessioned2024-04-04T02:37:15Z
dc.date.available2024-04-04T02:37:15Z
dc.date.issued2022-10
dc.identifier.issn0045-7930
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190789
dc.description.abstractEnIn this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration method for the shallow water equations. Due to the positivity-preserving property of mPDeC, the resulting scheme is unconditionally positivity preserving for the water height. To apply the mPDeC approach, we have to interpret the spatial semi-discretization in terms of production-destruction systems. Only small modifications inside the classical WENO implementation are necessary and we explain how it can be done. In numerical simulations, focusing on a fifth order method, we demonstrate the good performance of the new method and verify the theoretical properties.
dc.language.isoen
dc.publisherElsevier
dc.subject.enpositivity preserving
dc.subject.enwell-balanced
dc.subject.enWENO
dc.subject.enmodified Patankar
dc.subject.enshallow water
dc.subject.endeferred correction
dc.title.enAn arbitrary high order and positivity preserving method for the shallow water equations
dc.typeArticle de revue
dc.identifier.doi10.1016/j.compfluid.2022.105630
dc.subject.halMathématiques [math]
bordeaux.journalComputers and Fluids
bordeaux.page105630
bordeaux.volume247
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03893632
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03893632v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Computers%20and%20Fluids&rft.date=2022-10&rft.volume=247&rft.spage=105630&rft.epage=105630&rft.eissn=0045-7930&rft.issn=0045-7930&rft.au=CIALLELLA,%20M.&MICALIZZI,%20Lorenzo&%C3%96FFNER,%20Philipp&TORLO,%20Davide&rft.genre=article


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