OPERATOR SPLITTING BASED CENTRAL-UPWIND SCHEMES FOR SHALLOW WATER EQUATIONS WITH MOVING BOTTOM TOPOGRAPHY

Chertockj，Alina1; Kurganov，Alexander2; Wu，Tong3

2020

10.4310/CMS.2020.V18.N8.A3

Communications in Mathematical Sciences   影响因子和分区

1539-6746

1945-0796

In this paper, we develop a robust and efficient numerical method for shallow water equations with moving bottom topography. The model consists of the Saint-Venant system governing the water flow coupled with the Exner equation for the sediment transport. One of the main difficulties in designing good numerical methods for such models is related to the fact that the speed of water surface gravity waves is typically much faster than the speed at which the changes in the bottom topography occur. This imposes a severe stability restriction on the size of time steps, which, in turn, leads to excessive numerical diffusion that affects the computed bottom structure. In order to overcome this difficulty, we develop an operator splitting approach for the underlying coupled system, which allows one to treat slow and fast waves in a different manner and using different time steps. Our method is based on the application of a finite-volume central-upwind scheme introduced in [A. Kurganov and G. Petrova, Commun. Math. Sci., 5:133–160, 2007], and incorporates a staggered grid strategy needed for a proper approximation of the bottom topography function. A number of one- and two-dimensional numerical examples are presented to demonstrate the performance of the proposed method.

Exner equation moving bottom topography operator splitting method Saint Venant system of shallow water equations semi-discrete central-upwind schemes

英语

其他

2-s2.0-85099167501

Scopus

1.Department of Mathematics,North Carolina State University,Raleigh,27695,United States
2.Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Mathematics,The University of Texas at San Antonio,San Antonio,78249,United States

Chertockj，Alina,Kurganov，Alexander,Wu，Tong. OPERATOR SPLITTING BASED CENTRAL-UPWIND SCHEMES FOR SHALLOW WATER EQUATIONS WITH MOVING BOTTOM TOPOGRAPHY[J]. Communications in Mathematical Sciences,2020,18(8):2149-2168.

Chertockj，Alina,Kurganov，Alexander,&Wu，Tong.(2020).OPERATOR SPLITTING BASED CENTRAL-UPWIND SCHEMES FOR SHALLOW WATER EQUATIONS WITH MOVING BOTTOM TOPOGRAPHY.Communications in Mathematical Sciences,18(8),2149-2168.

Chertockj，Alina,et al."OPERATOR SPLITTING BASED CENTRAL-UPWIND SCHEMES FOR SHALLOW WATER EQUATIONS WITH MOVING BOTTOM TOPOGRAPHY".Communications in Mathematical Sciences 18.8(2020):2149-2168.