High-order compact gas-kinetic scheme for turbulence simulation

Developing high-order numerical schemes for compressible flow simulations remains a challenge, particularly when simultaneously resolving high-wavenumber waves and accurately capturing strong shock waves. Based on the time-accurate gas distribution function from the gas-kinetic scheme (GKS), the framework for high-order compact GKS (CGKS) has been developed. This approach integrates both numerical accuracy and physical consistency through direct numerical modelling of gas evolution in a discretized space. The CGKS achieves robustness, high accuracy, and larger explicit time steps than conventional compact schemes. The construction of the CGKS is characterized by: (1) high-order compact spatial reconstruction using only immediately adjacent cells; (2) high-order numerical flux calculation with nonlinear limiting; and (3) consistent flow variables evolution at cell interfaces to accommodate both smooth and discontinuous solutions. In summary, the CGKS offers an innovative method for devising high-order schemes for compressible flow simulations, leveraging the time-accurate evolution at cell interfaces to achieve robustness and accuracy.