High-order gas-kinetic scheme for numerical simulation of turbulence

We review the application of high-order gas-kinetic scheme (HGKS) in the numerical simulations of turbulence. HGKS was developed based on the two-stage fourth-order temporal discretization and high-order weighted essentially non-oscillation (WENO) reconstruction. Compared with the classical Riemann solvers, the high-order temporal evolution process, which is extremely helpful in the design of robust, accurate, and efficient higher-order schemes, can be used to construct a spatial-temporal coupled gas-kinetic flux solver. Currently, HGKS has been successfully applied in the direct numerical simulations and Reynolds averaged Navier-Stokes (RANS) simulations of turbulence, including low-speed turbulent channel flows, the decaying supersonic isotropic turbulence, the subsonic NACA0012 airfoil turbulence, and the transonic ARA M100 wing-body turbulence. The numerical results show that HGKS has the high accuracy and outstanding robustness for turbulence simulations. In summary, the HGKS provides a powerful computational tool for studying turbulent flows, especially for compressible turbulence. In the future, more challenging studies will be conducted, including the supersonic turbulent boundary layers and the shock-boundary layer interaction.