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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2021

A consistent quasi - second order staggered scheme for the two-dimensional shallow water equations

Résumé

A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in the discretisation cells while the vector unknowns are located on theedges (in 2D) or faces (in 3D) of the mesh. A MUSCL-like interpolation for the discrete convectionoperators in the water height and momentum equations is performed in order to improve the precisionof the scheme. The time discretization is performed either by a first order segregated forward Eulerscheme in time or by the second order Heun scheme. Both schemes are shown to preserve the waterheight positivity under a CFL condition and an important state equilibrium known as the lake at rest.Using some recent Lax-Wendroff type results for staggered grids, these schemes are shown to be Lax-consistent with the weak formulation of the continuous equations; besides, the forward Euler schemeis shown to be consistent with a weak entropy inequality. Numerical results confirm the efficiency andaccuracy of the schemes.
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Dates et versions

hal-02940981 , version 1 (16-09-2020)
hal-02940981 , version 2 (11-06-2021)
hal-02940981 , version 3 (17-11-2021)

Identifiants

Citer

R Herbin, J.-C Latché, Y Nasseri, N Therme. A consistent quasi - second order staggered scheme for the two-dimensional shallow water equations. IMA Journal of Numerical Analysis, In press, ⟨10.1093/imanum/drab086⟩. ⟨hal-02940981v3⟩
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