A second-order well-balanced scheme for the shallow-water equations with topography
LOUBÈRE, Raphaël
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
LOUBÈRE, Raphaël
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Communication dans un congrès
This item was published in
Springer Proceedings in Mathematics and Statistics, Springer Proceedings in Mathematics and Statistics, HYP2016, 2016-08-01, Aachen.
English Abstract
We consider the well-balanced numerical scheme for the shallow-water equations with topography introduced in [8] and its second-order well-balanced extension, which requires two heuristic parameters. The goal of the present ...Read more >
We consider the well-balanced numerical scheme for the shallow-water equations with topography introduced in [8] and its second-order well-balanced extension, which requires two heuristic parameters. The goal of the present contribution is to derive a parameter-free second-order well-balanced scheme. To that end, we consider a convex combination between the well-balanced scheme and a second-order scheme. We then prove that a relevant choice of the parameter of this convex combination ensures that the resulting scheme is both second-order accurate and well-balanced. Afterwards, we perform several numerical experiments, in order to illustrate both the second-order accuracy and the well-balance property of this numerical scheme. Finally, we outline some perspectives in a short conclusion.Read less <
ANR Project
Nouveaux schémas numériques pour des phénomènes géophysiques extrêmes - ANR-12-IS01-0004
MOdèles, Oscillations et SchEmas NUmeriques - ANR-14-CE23-0007
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
MOdèles, Oscillations et SchEmas NUmeriques - ANR-14-CE23-0007
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
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