Abstract:
Several high-order accurate gas-kinetic schemes (GKS) on unstructured meshes are briefly introduced, which are based on the efficient compact reconstruction using inner degree of freedom. They include two single-step schemes with third-order accuracy in space and time, developed with the combination of third-order GKS flux solver and the subcell finite volume scheme (SCFV) or the correction procedure via reconstruction (CPR) framework, respectively. The third one is the two-step forth-order CPR-GKS which is developed with the simple second-order GKS flux and two-step forth-order method. A hybrid of SCFV is then conducted to enhance the resolution of flow discontinuities and the three-dimensional scheme is further constructed on hexahedral meshes. Several typical flows are simulated for the comparative study of their high accuracy, high efficiency and good capability of discontinuity capturing in compressible flows. The multidimensional space and time evolution of GKS flux, as well as the high efficiency of compact reconstruction provide strong support for the development of high order schemes.