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Journal Articles International Journal on Finite Volumes Year : 2021

A well-defined moving steady states capturing Godunov-type scheme for Shallow-water model

Abstract

The present work concerns the derivation of a well-balanced scheme to approximate the weak solutions of the shallow-water model. Here, the numerical scheme exactly captures all the smooth steady solutions with nonvanishing velocities. To address such an issue, a Godunov-type scheme is adopted. A particular attention is paid on the derivation of the intermediate states within the approximate Riemann solver. Indeed, because of the moving steady states, the intermediate states may be ill-defined. Here, we introduce a suitable correction in order to get a fully well-defined finite volume scheme. In addition, the numerical method is established to be positive preserving and to satisfy a discrete entropy inequality up to small perturbations. Several numerical experiments, including wet/dry transition, illustrate the relevance of the designed scheme.
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Dates and versions

hal-03192954 , version 1 (08-04-2021)
hal-03192954 , version 2 (26-05-2021)

Identifiers

  • HAL Id : hal-03192954 , version 2

Cite

Christophe Berthon, Meissa M'Baye, Minh H. Le, Diaraf Seck. A well-defined moving steady states capturing Godunov-type scheme for Shallow-water model. International Journal on Finite Volumes, inPress. ⟨hal-03192954v2⟩
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