A High Order Central DG Method of the Two-Layer Shallow Water Equations

A High Order Central DG Method of the Two-Layer Shallow Water Equations

Year:    2020

Author:    Yongping Cheng, Haiyun Dong, Maojun Li, Weizhi Xian

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1437–1463

Abstract

In this paper, we focus on the numerical simulation of the two-layer shallow water equations over variable bottom topography. Although the existing numerical schemes for the single-layer shallow water equations can be extended to two-layer shallow water equations, it is not a trivial work due to the complexity of the equations. To achieve the well-balanced property of the numerical scheme easily, the two-layer shallow water equations are reformulated into a new form by introducing two auxiliary variables. Since the new equations are only conditionally hyperbolic and their eigenstructure cannot be easily obtained, we consider the utilization of the central discontinuous Galerkin method which is free of Riemann solvers. By choosing the values of the auxiliary variables suitably, we can prove that the scheme can exactly preserve the still-water solution, and thus it is a truly well-balanced scheme. To ensure the non-negativity of the water depth, a positivity-preserving limiter and a special approximation to the bottom topography are employed. The accuracy and validity of the numerical method will be illustrated through some numerical tests.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0155

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1437–1463

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Two-layer shallow water equations central DG method positivity-preserving and well-balanced still-water solution.

Author Details

Yongping Cheng

Haiyun Dong

Maojun Li

Weizhi Xian