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Low dispersion finite volume/element discretization of the enhanced Green-Naghdi equations for wave propagation, breaking and runup on unstructured meshes

hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorKAZOLEA, Maria
hal.structure.identifierBureau de Recherches Géologiques et Minières [BRGM]
dc.contributor.authorFILIPPINI, Andrea
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorRICCHIUTO, Mario
dc.date.accessioned2024-04-04T02:36:40Z
dc.date.available2024-04-04T02:36:40Z
dc.date.issued2023-04-01
dc.identifier.issn1463-5003
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190736
dc.description.abstractEnWe study a hybrid approach combining a FV and FE method to solve a fully nonlinear and weakly-dispersive depth averaged wave propagation model. The FV method is used to solve the underlying hyperbolic shallow water system, while a standard P 1 finite element method is used to solve the elliptic system associated to the dispersive correction. We study the impact of several numerical aspects: the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the well-posedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H 1. We show, based on both heuristic and strong numerical evidence, that numerical dissipation plays a major role in stabilizing the coupled method, and not only providing convergent results, but also providing the expected convergence rates. Finally, the full mode, coupling a wave breaking closure previously developed by the authors, is thoroughly tested on standard benchmarks using unstructured grids with sizes comparable or coarser than those usually proposed in literature.
dc.language.isoen
dc.publisherElsevier
dc.subject.enGreen-Naghdi equations
dc.subject.enHybrid scheme
dc.subject.enFinite Volumes
dc.subject.enFinite Elements
dc.subject.enHigh order
dc.subject.enWave breaking
dc.title.enLow dispersion finite volume/element discretization of the enhanced Green-Naghdi equations for wave propagation, breaking and runup on unstructured meshes
dc.typeArticle de revue
dc.identifier.doi10.1016/j.ocemod.2022.102157
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
bordeaux.journalOcean Modelling
bordeaux.page102157
bordeaux.volume182
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03402701
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03402701v1
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