Gas-Kinetic Methods for Turbulent Flow

Abstract

Gas-kinetic schemes are derived from the BGK-Boltzmann equation. These family of schemes for CFD are computationally more demanding than conventional upwind schemes but provide a number of advantages stemming precisely from the fact that they were not derived from the Navier–Stokes equations. We highlight three peculiarities: (i) the gas evolution is derived in space and time exactly, (ii) the viscous stress tensor is built from the collision operator and not through the diffusion operator, variations of the relaxation time are thus not simply applied linearly to the strain rate (and its moments) but input through the collision operator, (iii) the order of the Chapman–Enskog expansion is a “natural” way to further improve the physical consistence of the collision operator. In practice, gas-kinetic schemes are not only more suitable to resolve vortical structures but they also handle turbulent viscosity (or, better, a turbulent relaxation time) in a physically more relevant fashion. Whereas the first advantage is exploited mostly in approaches like Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), where the ability to resolve turbulent structures is key, the latter provides some leverage to approaches like Reynolds-Averaged Navier–Stokes (RANS) or hybrid RANS-LES where unresolved turbulence is funnelled through the collision operator. The paper aims at reviewing these advantages in the light of the results obtained by the author and those published in the recent years.