High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction

JOURNAL OF COMPUTATIONAL PHYSICS

卷:444

Article

Yang, Ruize¹  Yang, Yang²  Xing, Yulong¹ 

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

关键词: Shallow water equations;    Stiff friction terms;    Discontinuous Galerkin method;    Sign-preserving;    Well-balanced;    High order accuracy;   

DOI  :  10.1016/j.jcp.2021.110543

来源: Elsevier

【 摘 要 】

In this paper, we propose a family of second and third order temporal integration methods for systems of stiff ordinary differential equations, and explore their application in solving the shallow water equations with friction. The new temporal discretization methods come from a combination of the traditional Runge-Kutta method (for non-stiff equation) and exponential Runge-Kutta method (for stiff equation), and are shown to have both the sign-preserving and steady-state-preserving properties. They are combined with the well-balanced discontinuous Galerkin spatial discretization to solve the nonlinear shallow water equations with non-flat bottom topography and (stiff) friction terms. We have demonstrated that the fully discrete schemes satisfy the well-balanced, positivity-preserving and sign-preserving properties simultaneously. The proposed methods have been tested and validated on several one- and two-dimensional test cases, and good numerical results have been observed. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free