Numerical approximation of the shallow water equations with coriolis source term
We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the nu...
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doaj-80e46182b0804df6838db642fddf3d9c2021-07-15T14:18:27ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592021-01-0170314410.1051/proc/202107003proc2107003Numerical approximation of the shallow water equations with coriolis source termAudusse E.0Dubos V.1Duran A.2Gaveau N.3Nasseri Y.4Penel Y.5LAGA, Institut Galilée, Université Sorbonne Paris Nord — 99 avenue Jean-Baptiste ClémentINRIA Paris — Sorbonne Université — CNRS (LJLL), team ANGEInstitut Camille Jordan, Université Claude Bernard Lyon 1 —Institut Denis Poisson, Université D’OrléansInstitut de Mathématiques de Marseille, Université d’Aix-Marseille — Technopôle Château GombertINRIA Paris — Sorbonne Université — CNRS (LJLL), team ANGEWe investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.https://www.esaim-proc.org/articles/proc/pdf/2021/01/proc2107003.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Audusse E. Dubos V. Duran A. Gaveau N. Nasseri Y. Penel Y. |
spellingShingle |
Audusse E. Dubos V. Duran A. Gaveau N. Nasseri Y. Penel Y. Numerical approximation of the shallow water equations with coriolis source term ESAIM: Proceedings and Surveys |
author_facet |
Audusse E. Dubos V. Duran A. Gaveau N. Nasseri Y. Penel Y. |
author_sort |
Audusse E. |
title |
Numerical approximation of the shallow water equations with coriolis source term |
title_short |
Numerical approximation of the shallow water equations with coriolis source term |
title_full |
Numerical approximation of the shallow water equations with coriolis source term |
title_fullStr |
Numerical approximation of the shallow water equations with coriolis source term |
title_full_unstemmed |
Numerical approximation of the shallow water equations with coriolis source term |
title_sort |
numerical approximation of the shallow water equations with coriolis source term |
publisher |
EDP Sciences |
series |
ESAIM: Proceedings and Surveys |
issn |
2267-3059 |
publishDate |
2021-01-01 |
description |
We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes. |
url |
https://www.esaim-proc.org/articles/proc/pdf/2021/01/proc2107003.pdf |
work_keys_str_mv |
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