A High-Order Compact Gas-Kinetic Scheme in a Rotating Coordinates Frame and on Sliding Mesh

Abstract

This paper extends the high-order compact gas-kinetic scheme (CGKS) to flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis accelerations is used in the construction of the scheme. With the updates of both cell-averaged flow variables and their gradients in the rotating and stationary domains, a third-order compact reconstruction is developed with sliding interface between them. To capture shock waves and complicated wave interactions, the HWENO-type non-linear reconstruction and gradient compression factors are incorporated in the scheme. For achieving high-order time accuracy, based on the time-accurate flux function the multi-stage multi-derivative time stepping method is implemented in the scheme for the fourth-order time accuracy with two stages. The CGKS is validated in cases from subsonic acoustic wave propagation to high Mach number shock interaction. The compact scheme achieves high-order accuracy and remarkable robustness.