Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models

Cao, Yangyang1; Kurganov, Alexander2,3; Liu, Yongle1; Xin, Ruixiao1

2022-08-01

10.1007/s10915-022-01912-w

JOURNAL OF SCIENTIFIC COMPUTING   影响因子和分区

0885-7474

1573-7691

We extend recently proposed flux globalization based well-balanced path-conservative central-upwind schemes to several shallow water models including the Saint-Vevant system with and without the Manning friction term and rotating shallow water equations. We focus on development of the well-balanced schemes capable of exactly preserving quite complicated steady-state solutions the studied systems admit when the bottom topography is discontinuous. In such cases, nonconservative product terms naturally appear and they require a special treatment. To this end, we incorporate the nonconservative product terms into the global fluxes using the path-conservative technique implemented within a framework of simple-yet highly accurate and robust-Riemann-problem-solver-free central-upwind schemes. This results in new flux globalization based central-upwind schemes, which are more accurate than their existing counterparts. The advantages of the proposed schemes are demonstrated on a number of numerical examples.

Well-balanced schemes Flux globalization Path-conservative central-upwind schemes Nonconservative terms Shallow water models

SCI ; EI

英语

第一 ; 通讯

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

Mathematics

Mathematics, Applied

WOS:000822494100001

SPRINGER/PLENUM PUBLISHERS

20222812344596

Topography

Calculus:921.2 ; Materials Science:951

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China

Cao, Yangyang,Kurganov, Alexander,Liu, Yongle,et al. Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,92(2).

Cao, Yangyang,Kurganov, Alexander,Liu, Yongle,&Xin, Ruixiao.(2022).Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models.JOURNAL OF SCIENTIFIC COMPUTING,92(2).

Cao, Yangyang,et al."Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models".JOURNAL OF SCIENTIFIC COMPUTING 92.2(2022).