A Gradient Compression-Based Compact High-Order Gas-Kinetic Scheme on 3D Hybrid Unstructured Meshes

In this paper, a compact gas-kinetic scheme (CGKS) for compressible flow is constructed on hybrid unstructured mesh. Based on high-order gas evolution model at cell interfaces both cell-averaged flow variables and their gradients can be updated in CGKS and used in a compact third-order multi-resolution WENO reconstruction. In the precious CGKS, the flow variables at a cell interface are assumed to be continuous in space in the update of cell-averaged slopes. In order to improve the robustness of the scheme in discontinuous region in three-dimensional space, a compression factor for the cell-averaged gradients is proposed to take into account the possible discontinuity at cell interfaces. The accuracy of the scheme doesn't deteriorate with the implementation of the compression factor. Numerical tests from incompressible to hypersonic flow are presented to validate the high-order CGKS and demonstrate the effectiveness of the gradient compression factor for three-dimensional flow simulation on unstructured mesh.