Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes

Authors:
Jun Zhu;Jianxian Qiu;Chi-Wang Shu;Michael Dumbser
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, PR China and College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, PR China;Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, PR China;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;University of Trento, DICA Laboratory of Applied Mathematics, Via Mesiano,77 I-38050 Trento, Italy
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

In [J. Qiu, C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM Journal on Scientific Computing 26 (2005) 907-929], Qiu and Shu investigated using weighted essentially non-oscillatory (WENO) finite volume methodology as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods for solving nonlinear hyperbolic conservation law systems on structured meshes. In this continuation paper, we extend the method to solve two-dimensional problems on unstructured meshes, with the goal of obtaining a robust and high order limiting procedure to simultaneously obtain uniform high order accuracy and sharp, nonoscillatory shock transition for RKDG methods. Numerical results are provided to illustrate the behavior of this procedure.