Fifth-order A-WENO schemes based on the path-conservative central-upwind method

Chu，Shaoshuai1; Kurganov，Alexander2; Na，Mingye1

2022-11-15

10.1016/j.jcp.2022.111508

JOURNAL OF COMPUTATIONAL PHYSICS   Impact Factor & Quartile

0021-9991

1090-2716

We develop fifth-order A-WENO finite-difference schemes based on the path-conservative central-upwind method for nonconservative one- and two-dimensional hyperbolic systems of nonlinear PDEs. The main challenges in development of accurate and robust numerical methods for the studied systems come from the presence of nonconservative products. Semi-discrete second-order finite-volume path-conservative central-upwind (PCCU) schemes recently proposed in Castro Díaz et al. (2019) [8] provide one with a reliable Riemann-problem-solver-free numerical method for nonconservative hyperbolic system. In this paper, we extend the PCCU schemes to the fifth-order of accuracy in the framework of A-WENO finite-difference schemes. We apply the developed schemes to the two-layer shallow water equations. We ensure that the developed schemes are well-balanced in the sense that they are capable of exactly preserving “lake-at-rest” steady states. We illustrate the performance of the new fifth-order schemes on a number of one- and two-dimensional examples, where one can clearly see that the proposed fifth-order schemes clearly outperform their second-order counterparts.

A-WENO schemes Path-conservative central-upwind schemes Semi-discrete central-upwind schemes Two-layer shallow water equations Well-balanced schemes

EI

English

First ; Corresponding

National Natural Science Foundation of China[11771201];National Natural Science Foundation of China[12111530004];National Natural Science Foundation of China[12171226];Guangdong Provincial Key Laboratory Of Computational Science And Material Design[2019B030301001];

20223512627816

Equations of motion ; Finite difference method

Calculus:921.2 ; Numerical Methods:921.6

PHYSICS

2-s2.0-85136313887

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
2.Department of Mathematics,SUSTech International Center for Mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China

Chu，Shaoshuai,Kurganov，Alexander,Na，Mingye. Fifth-order A-WENO schemes based on the path-conservative central-upwind method[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,469.

Chu，Shaoshuai,Kurganov，Alexander,&Na，Mingye.(2022).Fifth-order A-WENO schemes based on the path-conservative central-upwind method.JOURNAL OF COMPUTATIONAL PHYSICS,469.

Chu，Shaoshuai,et al."Fifth-order A-WENO schemes based on the path-conservative central-upwind method".JOURNAL OF COMPUTATIONAL PHYSICS 469(2022).