Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

JOURNAL OF COMPUTATIONAL PHYSICS

卷:361

Article

Huang, Juntao¹  Shu, Chi-Wang² 

[1] Tsinghua Univ, Zhou Pei Yuan Ctr Appl Math, Beijing 100084, Peoples R China

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Discontinuous Galerkin method;    Scalar hyperbolic equations;    Stiff source;    Bound-preserving scheme;    High order accuracy;    Exponential Runge-Kutta method;   

DOI  :  10.1016/j.jcp.2018.01.051

来源: Elsevier

【 摘 要 】

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free