A Two-Stage Fourth-Order Gas-Kinetic CPR Method for Subsonic Flows on Hexahedral Meshes

A compact high-order gas-kinetic scheme (GKS) is developed for three dimensional subsonic inviscid and viscous flows on hexahedral meshes, which achieves fourth-order accuracy in both space and time. The scheme combines a compact and efficient correction procedure via reconstruction (CPR) framework with a time-evolving gas-kinetic flux, in which the inviscid and viscous fluxes are coupled and computed uniformly. With the CPR framework, the current scheme avoids the difficulty of compact fourth-order reconstruction encountered by the traditional finite volume GKS. Moreover, both the flux and its time-derivative are available in the gas kinetic flux so that an efficient two-stage temporal discretization can be adopted to achieve fourth-order time accuracy, which is more efficient than the traditional Runge-Kutta CPR method. In addition, with the help of isoparametric transformation, the current scheme can treat curved boundaries with high-order curved meshes. Typical numerical tests demonstrate the good performance of the current scheme.