Gas kinetic scheme for turbulence simulation

The extended gas-kinetic scheme (GKS) for turbulence simulations is developed based on the generalized BGK equation with the effective relaxation time. This relaxation time can be computed from the turbulent viscosity, through which turbulence models can be directly combined. For engineering low-cost simulations of high Reynolds number flows, common-used RANS models are applied, while the LES and hybrid RANS/LES (DES and IDDES) models as well as the minimized dispersion and controllable dissipation (MDCD) reconstruction are adopted in high fidelity turbulence simulations. In addition, the turbulent transport equations are solved in a strongly coupled way by using GKS with scalar transport. The extended GKS is applied in typical turbulent flow predictions including the RANS simulation of hypersonic compression ramp flow and the detailed simulation of multiscale turbulent structures in low-speed cylinder flow with hybrid models. The predicted results agree well with existing experimental measurements and numerical studies, which shows the good accuracy, resolution and robustness of the extended GKS and reveals the wide prospects in turbulence simulations on different model scales, including the multiscale models such as hybrid RANS/LES methods. Furthermore, the multiscale turbulence simulation methods are worthy of further studies based on the generalized BGK model.