Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier-Stokes equations

In this paper, a third order gas kinetic scheme is developed on the three dimensional hybrid unstructured meshes for the numerical simulation of compressible inviscid and viscous flows. A third-order WENO reconstruction is developed on the hybrid unstructured meshes, including tetrahedron, pyramid, prism and hexahedron. A simple strategy is adopted for the selection of big stencil and sub-stencils. Incorporate with the two-stage fourth-order temporal discretization and lower-upper symmetric Gauss-Seidel methods, both explicit and implicit high-order gas-kinetic schemes are developed. A variety of numerical examples, from the subsonic to supersonic flows, are presented to validate the accuracy and robustness for both inviscid and viscous flows.