A high-order compact gas-kinetic scheme in a rotating coordinate frame and on sliding mesh

TL;DR

This paper develops a high-order compact gas-kinetic scheme tailored for compressible flows in rotating frames, incorporating advanced reconstruction and time-stepping methods, validated across diverse flow scenarios.

Contribution

It introduces a third-order compact scheme with sliding interfaces and fourth-order time accuracy for rotating frame flows, combining HWENO reconstruction and MSMD time stepping.

Findings

Achieves high-order accuracy and robustness in rotating frame flows.

Effectively captures shock waves and wave interactions.

Validated on a range of test cases from subsonic to high Mach numbers.

Abstract

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