一种维持Saint-Venant方程组移动稳态解的中心格式

Abstract

Abstract:

In this paper, we propose a second-order unstaggered central finite volume scheme for the Saint-Venant system. Classical central scheme can preserve still-water steady state solution by reconstructing conservative variables and the water level, but generates enormous numerical oscillation when considering moving-water steady state. We choose to reconstruct conservative variables and the energy, and design a new discretization of the source term to preserve moving-water equilibria and capture its small perturbations. In the end, several classical numerical experiments are performed to verify the proposed scheme which is convergent, well-balanced and robust.

Key words: Saint-Venant system, Unstaggered central scheme, Moving-water equilibria

CLC Number:

O241.82

Yiming Luo,Dingfang Li,Min Liu,Jian Dong. Moving-Water Equilibria Preserving Central Scheme for the Saint-Venant System[J].Acta mathematica scientia,Series A, 2022, 42(3): 891-903.

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References 17

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网格数	$L^1$误差	收敛阶
50	$6.26*10^{-4}$	-
100	$1.57*10^{-4}$	2.00
200	$3.90*10^{-5}$	2.01
400	$9.73*10^{-6}$	2.00

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Moving-Water Equilibria Preserving Central Scheme for the Saint-Venant System

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