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Maximum-Principle-Satisfying and Positivity-Preserving High Order Central DG Methods on Unstructured Overlapping Meshes for Two-Dimensional Hyperbolic Conservation Laws

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Abstract

In this paper, we first present a family of high order central discontinuous Galerkin methods defined on unstructured overlapping meshes for the two-dimensional conservation laws. The primal mesh is a triangulation of the computational domain, while the dual mesh is a quadrangular partition which is formed by connecting an interior point and the three vertexes of each triangle on the primal mesh. We prove the \(L^2\) stability of the present method for linear equation. Then we design and analyze high order maximum-principle-satisfying central discontinuous Galerkin methods for two-dimensional scalar conservation law, and high order positivity-preserving central discontinuous Galerkin methods for two-dimensional compressible Euler systems. The performance of the proposed methods is finally demonstrated through a set of numerical experiments.

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Acknowledgements

ML is partially supported by a NSFC (Grant No. 11501062, 11871139). HD is partially supported by a NSFC (Grant No. 11701055). LX is partially supported by a Key Project of the Major Research Plan of NSFC (Grant No. 91630205) and a NSFC (Grant No. 11771068).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Maojun Li & Liwei Xu

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Haiyun Dong & Binbin Hu

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  1. Maojun Li
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  2. Haiyun Dong
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  3. Binbin Hu
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  4. Liwei Xu
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Correspondence to Liwei Xu.

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Li, M., Dong, H., Hu, B. et al. Maximum-Principle-Satisfying and Positivity-Preserving High Order Central DG Methods on Unstructured Overlapping Meshes for Two-Dimensional Hyperbolic Conservation Laws. J Sci Comput 79, 1361–1388 (2019). https://doi.org/10.1007/s10915-018-00895-x

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