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Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes

Jun Zhu Nanjing University of Aeronautics and Astronautics Xinghui Zhong Michigan State University Chi-Wang Shu Brown University Jianxian Qiu Xiamen University

Numerical Analysis and Scientific Computing mathscidoc:1610.25056

Journal of Computational Physics, 248, 200-220, 2013
In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
Runge-Kutta discontinuous Galerkin method, limiter, WENO finite volume methodology
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@inproceedings{jun2013runge-kutta,
  title={ Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes},
  author={Jun Zhu, Xinghui Zhong, Chi-Wang Shu, and Jianxian Qiu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012060028275742174},
  booktitle={Journal of Computational Physics},
  volume={248},
  pages={200-220},
  year={2013},
}
Jun Zhu, Xinghui Zhong, Chi-Wang Shu, and Jianxian Qiu. Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes. 2013. Vol. 248. In Journal of Computational Physics. pp.200-220. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012060028275742174.
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