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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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.
KeywordsConservation laws Central discontinuous Galerkin methods Unstructured overlapping meshes Maximum principle Positivity preserving
Mathematics Subject Classification65M60 76M10
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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