Commun. Comput. Phys., 11 (2012), pp. 985-1005.


Runge-Kutta Discontinuous Galerkin Method Using WENO-Type Limiters: Three-Dimensional Unstructured Meshes

Jun Zhu 1, Jianxian Qiu 2*

1 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, P.R. China.
2 School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P.R. China and Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, P.R. China.

Received 30 August 2010; Accepted (in revised version) 24 May 2011
Available online 18 November 2011
doi:10.4208/cicp.300810.240511a

Abstract

This paper further considers weighted essentially non-oscillatory (WENO) and Hermite weighted essentially non-oscillatory (HWENO) finite volume methods as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve problems involving nonlinear hyperbolic conservation laws. The application discussed here is the solution of 3-D problems on unstructured meshes. Our numerical tests again demonstrate this is a robust and high order limiting procedure, which simultaneously achieves high order accuracy and sharp non-oscillatory shock transitions.

AMS subject classifications: 65M06, 65M99, 35L65

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Key words: Runge-Kutta discontinuous Galerkin method, limiter, WENO, HWENO, high order limiting procedure.

*Corresponding author.
Email: zhujun@nuaa.edu.cn (J. Zhu), jxqiu@xmu.edu.cn, jxqiu@nju.edu.cn (J. Qiu)
 

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