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

摘要

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 L2 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.