A gas - kinetic scheme for turbulent flow

A gas-kinetic scheme is used in this study to simulate turbulent flow and the interaction between a shock wave and a turbulent boundary layer in particular. Gas-kinetic schemes belong to a class of their own of numerical schemes for fluid mechanics. These schemes are neither particle methods, such as DSMC and Molecular Dynamics, nor Lattice Boltzmann methods: they calculate the fluxes between numerical cells on the basis of the Boltzmann equation instead of the Navier-Stokes or Euler equations. Advective and viscous fluxes are coupled in gas-kinetic schemes; in other words, the effect of unresolved fluctuations (represented in conventional schemes by the viscous fluxes) may affect the transport terms (advection). In simulations of turbulent flow where the unresolved turbulent fluctuations are modeled by eddy viscosity, a gas-kinetic scheme may “exploit” the information provided by the turbulence model in a different way. The analysis proposed in this paper shows that gas-kinetic schemes have an in-built “multiscalar” sensor which controls the correction terms generated by the underlying kinetic theory. The simulations shown in this paper have been obtained with the RANS approach and a standard two-equation turbulence model (k-ω). It is shown that the gas-kinetic scheme provides good quality predictions in a number of test cases, where conventional schemes with the same turbulence model are known to fail