A gas-kinetic scheme for the simulation of turbulent flow

A BGK gas-kinetic scheme may simulate turbulent flow, provided the relaxation time is defined in such a way, that it accounts for the unresolved turbulent fluctuations. In this study, a simple turbulent gas-kinetic scheme is developed by coupling the evolution of conservative variables to a two-equation turbulence model. Its behavior is compared to the one of conventional schemes, based on the Navier-Stokes equations, by simulating turbulent flow cases with strong interactions between shocks and boundary layer. Whereas conventional schemes are known to fail, or to be rather inaccurate, the turbulent gas-kinetic scheme provides results which are consistently good or at least acceptable for engineering standards. It is argued, that gas-kinetic schemes have an in-built “multiscale” sensor which correct advection whenever the ratio of unresolved to resolved scales of motion raises above negligible values