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On the Numerical Solution of Sparse Linear Systems Emerging in Finite Volume Discretizations of 2D Boussinesq-Type Models on Unstructured Grids

hal.structure.identifierTechnical University of Crete [Chania] [TUC]
dc.contributor.authorDELIS, Anargiros
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorKAZOLEA, Maria
hal.structure.identifierTechnical University of Crete [Chania] [TUC]
dc.contributor.authorGAITANI, Maria
dc.date.accessioned2024-04-04T02:39:42Z
dc.date.available2024-04-04T02:39:42Z
dc.date.issued2022-11-07
dc.identifier.issn2073-4441
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190997
dc.description.abstractEnThis work aims to supplement the realization and validation of a higher-order well-balanced unstructured finite volume (FV) scheme, that has been relatively recently presented, for numerically simulating weakly non-linear weakly dispersive water waves over varying bathymetries. We in-vestigate and develop solution strategies for the sparse linear system that appears during this FV discretisation of a set of extended Boussinesq-type equations on unstructured meshes. The resultant linear system of equations must be solved at each discrete time step as to recover the actual velocity field of the flow and advance in time. The system’s coefficient matrix is sparse, un-symmetric and often ill-conditioned. Its characteristics are affected by physical quantities of the problem to be solved, such as the undisturbed water depth and the mesh topology. To this end, we investigate the application of different well-known iterative techniques, with and without the usage of preconditioners and reordering, for the solution of this sparse linear system. The iiterative methods considered are the GMRES and the BiCGSTAB, three preconditioning techniques, including different ILU factorizations and two different reordering techniques are implemented and discussed. An optimal strategy, in terms of computational efficiency and robustness, is finally proposed which combines the use of the BiCGSTAB method with the ILUT preconditioner and the Reverse Cuthill–McKee reordering.
dc.language.isoen
dc.publisherMDPI
dc.subject.enBoussinesq-type equations
dc.subject.enfinite volumes
dc.subject.enunstructured meshes
dc.subject.ensparse matrices
dc.subject.enpreconditioning
dc.subject.enreordering
dc.title.enOn the Numerical Solution of Sparse Linear Systems Emerging in Finite Volume Discretizations of 2D Boussinesq-Type Models on Unstructured Grids
dc.typeArticle de revue
dc.identifier.doi10.3390/w14213584
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalWater
bordeaux.page3584
bordeaux.volume14
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue21
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03842176
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03842176v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Water&rft.date=2022-11-07&rft.volume=14&rft.issue=21&rft.spage=3584&rft.epage=3584&rft.eissn=2073-4441&rft.issn=2073-4441&rft.au=DELIS,%20Anargiros&KAZOLEA,%20Maria&GAITANI,%20Maria&rft.genre=article


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