A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System

Chen, Xi1,2; Kurganov, Alexander3,4

2023-05-01

10.4208/cicp.OA-2022-0319

COMMUNICATIONS IN COMPUTATIONAL PHYSICS   影响因子和分区

1815-2406

1991-7120

We develop a new moving-water equilibria preserving partial relaxation (PR) scheme for the two-dimensional (2-D) Saint-Venant system of shallow water equations. The new scheme is a 2-D generalization of the one-dimensional (1-D) PR scheme recently proposed in [X. Liu, X. Chen, S. Jin, A. Kurganov, and H. Yu, SIAM J. Sci. Comput., 42 (2020), pp. A2206-A2229]. Our scheme is based on the PR approximation, which is designed in two steps. First, the geometric source terms are incorporated into the discharge fluxes, which results in a hyperbolic system with global fluxes. Second, the discharge equations are relaxed so that the nonlinearity is moved into the stiff right-hand side of the four added auxiliary equation. The obtained PR system is then numerically integrated using a semi-discrete hybrid upwind/central-upwind finitevolume method combined with an efficient semi-implicit ODE solver. The new 2-D PR scheme inherits the main advantages of the 1-D PR scheme: (i) no special treatment of the geometric source terms is required, (ii) no nonlinear (cubic) equations should be solved to obtain the point values of the water depth out of the reconstructed equilibrium variables. The performance of the proposed PR scheme is illustrated on a number of numerical examples, in which we demonstrate that the PR scheme not only capable of exactly preserving quasi 1-D moving-water steady states and accurately capturing their small perturbations, but can also handle genuinely 2-D steady states and their small perturbations in a non-oscillatory manner.

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

SCI

英语

通讯

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

Physics

Physics, Mathematical

WOS:001016172500008

GLOBAL SCIENCE PRESS

Web of Science

1.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, SUSTech 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

Chen, Xi,Kurganov, Alexander. A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2023,33(5).

Chen, Xi,&Kurganov, Alexander.(2023).A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,33(5).

Chen, Xi,et al."A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 33.5(2023).