Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system

Kurganov，Alexander1; Qu，Zhuolin2; Wu，Tong2

2022-06-27

10.1051/m2an/2022041

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS   Impact Factor & Quartile

2822-7840

2804-7214

We extend the adaptive moving mesh (AMM) central-upwind schemes recently proposed in Kurganov et al. [Commun. Appl. Math. Comput. 3 (2021) 445-479] in the context of one- (1-D) and two-dimensional (2-D) Euler equations of gas dynamics and granular hydrodynamics, to the 1-D and 2-D Saint-Venant system of shallow water equations. When the bottom topography is nonflat, these equations form hyperbolic systems of balance laws, for which a good numerical method should be capable of preserving a delicate balance between the flux and source terms as well as preserving the nonnegativity of water depth even in the presence of dry or almost dry regions. Therefore, in order to extend the AMM central-upwind schemes to the Saint-Venant systems, we develop special positivity preserving reconstruction and evolution steps of the AMM algorithms as well as special corrections of the solution projection step in (almost) dry areas. At the same time, we enforce the moving mesh to be structured even in the case of complicated 2-D computational domains. We test the designed method on a number of 1-D and 2-D examples that demonstrate robustness and high resolution of the proposed numerical approach.

Adaptive moving mesh methods Saint-Venant systems of shallow water equations finite-volume methods well-balanced methods positivity preserving methods central-upwind schemes moving mesh differential equations

SCI ; EI

English

First ; Corresponding

NSFC["11771201","12111530004","12171226"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Mathematics

Mathematics, Applied

WOS:000823640000008

EDP SCIENCES S A

20222712317856

Equations of motion ; Gas dynamics ; Mesh generation ; Numerical methods ; One dimensional ; Topography

Gas Dynamics:631.1.2 ; Computer Applications:723.5 ; Calculus:921.2 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4 ; Numerical Methods:921.6 ; Materials Science:951

MATHEMATICS

2-s2.0-85133270180

Web of Science

1.Department of Mathematics,SUSTech Intl. Ctr. for Math. and Guangdong Prov. Key Lab. of Compl. Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
2.Department of Mathematics,University of Texas at San Antonio,San Antonio,78249,United States

Kurganov，Alexander,Qu，Zhuolin,Wu，Tong. Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS,2022,56(4):1327-1360.

Kurganov，Alexander,Qu，Zhuolin,&Wu，Tong.(2022).Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS,56(4),1327-1360.

Kurganov，Alexander,et al."Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS 56.4(2022):1327-1360.