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.A CONSISTENT QUASI - SECOND ORDER STAGGERED SCHEME FORTHE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02940981
Contributor : Raphaele Herbin <>
Submitted on : Friday, June 11, 2021 - 4:31:13 PM
Last modification on : Wednesday, June 16, 2021 - 3:35:33 AM

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  • HAL Id : hal-02940981, version 2

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R Herbin, J.-C Latché, Y Nasseri, N Therme. .A CONSISTENT QUASI - SECOND ORDER STAGGERED SCHEME FORTHE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS. 2021. ⟨hal-02940981v2⟩

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