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A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids

hal.structure.identifierDepartment of Applied Mathematics
dc.contributor.authorVILAR, François
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine [CESTA]
dc.contributor.authorMAIRE, P.H.
hal.structure.identifierParallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
dc.contributor.authorABGRALL, Remi
dc.date.accessioned2024-04-15T09:41:41Z
dc.date.available2024-04-15T09:41:41Z
dc.date.created2014-01-08
dc.date.issued2014-02-21
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/197621
dc.description.abstractPartant de la description cinématique en coordonnées de Lagrange, on développe un schéma pour la dynamique des gaz 2D sur des maillages non struturés. Ici, on emploie une formulation en coordonnées de Lagrange totale, c
dc.description.abstractEnBased on the total Lagrangian kinematical description, a discontinuous Galerkin (DG) discretization of the gas dynamics equations is developed for two-dimensional fluid flows on general unstructured grids. Contrary to the updated Lagrangian formulation, which refers to the current moving configuration of the flow, the total Lagrangian formulation refers to the reference fixed configuration, which is usually the initial one. In this framework, the Lagrangian and Eulerian descriptions of the kinematical and the physical variables are related by means of the Piola transformation. Here, we describe a cell-centered high-order DG discretization of the physical conservation laws. The geometrical conservation law, which governs the time evolution of the deformation gradient, is solved by means of a finite element discretization. This approach allows to satisfy exactly the Piola compatibility condition. Regarding the DG approach, it relies on the use of a polynomial space approximation which is spanned by a Taylor basis. The main advantage in using this type of basis relies on its adaptability regardless the shape of the cell. The numerical fluxes at the cell interfaces are computed employing a node-based solver which can be viewed as an approximate Riemann solver. We present numerical results to illustrate the robustness and the accuracy up to third-order of our DG method. First, we show its ability to accurately capture geometrical features of a flow region employing curvilinear grids. Second, we demonstrate the dramatic improvement in symmetry preservation for radial flows.
dc.language.isoen
dc.title.enA discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
dc.typeRapport
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]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.type.institutionINRIA
bordeaux.type.reportrr
hal.identifierhal-00950782
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00950782v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2014-02-21&rft.au=VILAR,%20Fran%C3%A7ois&MAIRE,%20P.H.&ABGRALL,%20Remi&rft.genre=unknown


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