MOVING-WATER EQUILIBRIA PRESERVING PARTIAL RELAXATION SCHEME FOR THE SAINT-VENANT SYSTEM

Liu, Xin1,2; Chen, Xi1,3; Jin, Shi4; Kurganov, Alexander1,5; Wu, Tong6; Yu, Hui7

2020

10.1137/19M1258098

SIAM JOURNAL ON SCIENTIFIC COMPUTING   影响因子和分区

1064-8275

1095-7197

We develop a new moving-water equilibria preserving numerical scheme for the Saint-Venant system. The new scheme is designed in two major steps. First, the geometric source term is incorporated into the discharge flux, which results in a hyperbolic system with a global flux. Second, the discharge equation is relaxed so that the nonlinearity is moved into the stiff right-hand side of the added auxiliary equation. The main advantages of the new scheme are that (i) no special treatment of the geometric source term is required, and (ii) no nonlinear (cubic) equations should be solved to obtain the point values of the water depth out of the reconstructed equilibrium variables, as it must be done in the existing alternative methods. We also develop a hybrid numerical flux, which helps to handle various flow regimes in a stable manner. Several numerical experiments are performed to verify that the proposed scheme is capable of exactly preserving general moving-water steady states and accurately capturing their small perturbations.

Saint-Venant system of shallow water equations partial relaxation scheme well-balanced method steady-state solutions (equilibria) moving-water and still-water equilibria

SCI ; EI

英语

第一 ; 通讯

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

Mathematics

Mathematics, Applied

WOS:000568184400012

SIAM PUBLICATIONS

20204009298865

Equations of motion ; Nonlinear equations

Control Systems:731.1 ; Calculus:921.2

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Environm & Climate Change Canada, Canadian Meteorol Ctr, Numer Environm Predict Sect, Dorval, PQ H9P 1J3, Canada
3.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
4.Shanghai Jiao Tong Univ, Sch Math Sci, Inst Nat Sci, MOE LSC, Shanghai 200240, Peoples R China
5.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China
6.Tulane Univ, Math Dept, New Orleans, LA 70118 USA
7.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

Liu, Xin,Chen, Xi,Jin, Shi,et al. MOVING-WATER EQUILIBRIA PRESERVING PARTIAL RELAXATION SCHEME FOR THE SAINT-VENANT SYSTEM[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(4):A2206-A2229.

Liu, Xin,Chen, Xi,Jin, Shi,Kurganov, Alexander,Wu, Tong,&Yu, Hui.(2020).MOVING-WATER EQUILIBRIA PRESERVING PARTIAL RELAXATION SCHEME FOR THE SAINT-VENANT SYSTEM.SIAM JOURNAL ON SCIENTIFIC COMPUTING,42(4),A2206-A2229.

Liu, Xin,et al."MOVING-WATER EQUILIBRIA PRESERVING PARTIAL RELAXATION SCHEME FOR THE SAINT-VENANT SYSTEM".SIAM JOURNAL ON SCIENTIFIC COMPUTING 42.4(2020):A2206-A2229.