Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system
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.
First ; Corresponding
NSFC["11771201","12111530004","12171226"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]
|WOS Research Area|
|WOS Accession No|
|EI Accession Number|
Equations of motion ; Gas dynamics ; Mesh generation ; Numerical methods ; One dimensional ; Topography
|ESI Classification Code|
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
|ESI Research Field|
Web of Science
Cited Times [WOS]:0
|Document Type||Journal Article|
|Department||Department of Mathematics|
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
|First Author Affilication||Department of Mathematics|
|Corresponding Author Affilication||Department of Mathematics|
|First Author's First Affilication||Department of Mathematics|
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.
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