Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy

Chen, Xi1,5; Kurganov, Alexander3,4; Liu, Yongle2,5

2023-06-01

10.1007/s10915-023-02221-6

JOURNAL OF SCIENTIFIC COMPUTING   影响因子和分区

0885-7474

1573-7691

We develop flux globalization based well-balanced central-upwind schemes for hydrodynamic equations with general free energy. The proposed schemes are well-balanced in the sense that they are capable of exactly preserving quite complicated steady-state solutions and also exactly capturing traveling waves, even when vacuum regions are present. In order to accurately track interfaces of the vacuum regions and near vacuum parts of the solution, we use the technique introduced in Chertock et al. (J Sci Comput 90:Paper No. 9, 2022) and design a hybrid approach: inside the no vacuum regions, we use the flux globalization based well-balanced central-upwind scheme, while elsewhere we implement the central-upwind scheme similar to the one proposed in Bollermann et al. (J Sci Comput 56:267-290, 2013) in the context of wet/dry fronts in the shallow water equations. The advantages of the proposed schemes are demonstrated on a number of challenging numerical examples.

Hydrodynamic equations with general free energy Well-balanced schemes Flux globalization Central-upwind schemes Vacuum regions

SCI ; EI

英语

通讯

NSFC["12111530004","12171226"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001] ; SNF["200020_204917","FZEB-0-166980"]

Mathematics

Mathematics, Applied

WOS:000986495200001

SPRINGER/PLENUM PUBLISHERS

20232014100251

Equations of motion ; Hydrodynamics

Thermodynamics:641.1 ; Calculus:921.2

MATHEMATICS

Web of Science

1.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
2.Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
3.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Dept Math, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

Chen, Xi,Kurganov, Alexander,Liu, Yongle. Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy[J]. JOURNAL OF SCIENTIFIC COMPUTING,2023,95(3).

Chen, Xi,Kurganov, Alexander,&Liu, Yongle.(2023).Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy.JOURNAL OF SCIENTIFIC COMPUTING,95(3).

Chen, Xi,et al."Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy".JOURNAL OF SCIENTIFIC COMPUTING 95.3(2023).