Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:421

Article

Zhao, Weifeng¹  Huang, Juntao²  Ruuth, Steven J.³ 

[1] Univ Sci & Technol Beijing, Dept Appl Math, Beijing 100083, Peoples R China

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[3] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

关键词: Hyperbolic conservation laws;    High order RK methods;    Boundary treatment;    Downwind spatial discretization;    Inverse Lax-Wendroff;   

DOI  :  10.1016/j.jcp.2020.109697

来源: Elsevier

【 摘 要 】

In [4], we developed a boundary treatment method for implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK methods include explicit ones as special cases, this boundary treatment method naturally applies to explicit methods as well. In this paper, we examine this boundary treatment method for the case of explicit RK schemes of arbitrary order applied to hyperbolic conservation laws. We show that the method not only preserves the accuracy of explicit RK schemes but also possesses good stability. This compares favorablyto the inverse Lax-Wendroff method in [5,6] where analysis and numerical experiments have previously verified the presence of order reduction [5,6]. In addition, we demonstrate that our method performs well for strong-stability-preserving (SSP) RK schemes involving negative coefficients and downwind spatial discretizations. It is numerically shown that when boundary conditions are present and the proposed boundary treatment is used, that SSP RK schemes with negative coefficients still allow for larger time steps than schemes with all nonnegative coefficients. In this regard, our boundary treatment method is an effective supplement to SSP RK schemes with/without negative coefficients for initial-boundary value problems for hyperbolic conservation laws. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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