A WELL-BALANCED ASYMPTOTIC PRESERVING SCHEME FOR THE TWO-DIMENSIONAL ROTATING SHALLOW WATER EQUATIONS WITH NONFLAT BOTTOM TOPOGRAPHY

Kurganov，Alexander1; Liu，Yongle2,3; Lukáčová-Medviďová，Mária4

2022

10.1137/21M141573X

SIAM JOURNAL ON SCIENTIFIC COMPUTING   影响因子和分区

1064-8275

1095-7197

We consider the two-dimensional rotating shallow water equations with nonflat bottom topography. We focus on the case of low Froude number, in which the system is stiff and conventional explicit numerical methods are extremely inefficient and often impractical. Our goal is to design a finite volume scheme, which is both asymptotic preserving (uniformly asymptotically consistent and stable for a broad range of low Froude numbers) and well-balanced (capable of exactly preserving geophysically relevant steady-state solutions). The goal is achieved in two steps. We first rewrite the studied equations in terms of perturbations of the steady state and then apply the flux splitting similar to the one used in [Liu, Chertok, and Kurganov J. Comput. Phys., 391 (2019), pp. 259-279]. We split the flux into the stiff and nonstiff parts and then use an implicit-explicit approach: apply an explicit second-order central-upwind scheme to the nonstiff part of the system while treating the stiff part implicitly. As the stiff part of the flux is linear, we reduce the implicit stage of the proposed method to solving a Poisson-type elliptic equation, which is discretized using a standard second-order central difference scheme. We prove the asymptotic preserving property of the developed scheme and conduct a series of numerical experiments, which demonstrate that our scheme outperforms the non-well-balanced asymptotic preserving scheme from [Liu, Chertok, and Kurganov J. Comput. Phys., 391 (2019), pp. 259-279].

asymptotic preserving scheme central-upwind scheme flux splitting implicit-explicit approach rotating shallow water equations well-balanced scheme

SCI ; EI

英语

第一

National Natural Science Foundation of China[11771201];National Natural Science Foundation of China[1201101343];National Natural Science Foundation of China[12171226];

Mathematics

Mathematics, Applied

WOS:000862824700012

SIAM PUBLICATIONS

20223112531922

Equations of motion ; Numerical methods ; Poisson equation ; Topography

Fluid Flow, General:631.1 ; Calculus:921.2 ; Numerical Methods:921.6 ; Materials Science:951

MATHEMATICS

2-s2.0-85135228014

Scopus

1.Department of Mathematics,SUSTech International Center for Mathematics,Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
2.Department of Mathematics,Harbin Institute of Technology,Harbin,150001,China
3.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
4.Institute of Mathematics,University of Mainz,Mainz,Germany

Kurganov，Alexander,Liu，Yongle,Lukáčová-Medviďová，Mária. A WELL-BALANCED ASYMPTOTIC PRESERVING SCHEME FOR THE TWO-DIMENSIONAL ROTATING SHALLOW WATER EQUATIONS WITH NONFLAT BOTTOM TOPOGRAPHY[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2022,44(3):A1655-A1680.

Kurganov，Alexander,Liu，Yongle,&Lukáčová-Medviďová，Mária.(2022).A WELL-BALANCED ASYMPTOTIC PRESERVING SCHEME FOR THE TWO-DIMENSIONAL ROTATING SHALLOW WATER EQUATIONS WITH NONFLAT BOTTOM TOPOGRAPHY.SIAM JOURNAL ON SCIENTIFIC COMPUTING,44(3),A1655-A1680.

Kurganov，Alexander,et al."A WELL-BALANCED ASYMPTOTIC PRESERVING SCHEME FOR THE TWO-DIMENSIONAL ROTATING SHALLOW WATER EQUATIONS WITH NONFLAT BOTTOM TOPOGRAPHY".SIAM JOURNAL ON SCIENTIFIC COMPUTING 44.3(2022):A1655-A1680.