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Article Dans Une Revue Communications in Mathematical Sciences Année : 2022

A fully well-balanced scheme for shallow water equations with Coriolis force

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Résumé

The present work is devoted to the derivation of a fully well-balanced and positivity-preserving numerical scheme for the shallow water equations with Coriolis force. The first main issue consists in preserving all the steady states. Our strategy relies on a Godunov-type scheme with suitable source term and steady state discretisations. The preservation of moving steady states may lead to ill-defined intermediate states in the Riemann solver. Therefore, a proper correction is introduced in order to obtain a fully well-balanced scheme. The second challenge lies in improving the order of the scheme while preserving the fully well-balanced property. A modification of the classical methods is required since no conservative reconstruction can preserve all the steady states in the case of rotating shallow water equations. A steady state detector is used to overcome this matter. Some numerical experiments are presented to show the relevance and accuracy of both first-order and second-order schemes.

Dates et versions

hal-03880393 , version 1 (01-12-2022)

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Vivien Desveaux, Alice Masset. A fully well-balanced scheme for shallow water equations with Coriolis force. Communications in Mathematical Sciences, 2022, 20 (7), pp.1875-1900. ⟨10.4310/CMS.2022.v20.n7.a4⟩. ⟨hal-03880393⟩
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