A Modified Gas-Kinetic Scheme for Turbulent Flow

By analogy with the kinetic theory of gases, most turbulence modeling strate- gies rely on an eddy viscosity to model the unresolved turbulent fluctuations. How- ever, the ratio of unresolved to resolved scales - very much like a degree of rarefaction - is not taken into account by the popular conventional schemes, based on the Navier- Stokes equations. This paper investigates the simulation of turbulent flow with a gas- kinetic scheme. In so doing, the modeling of turbulence becomes part of the numerical scheme: the degree of rarefaction is automatically taken into account; the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any as- sumptions on the type of turbulence or flow class. The implementation of a turbulent gas-kinetic scheme into a finite-volume solver is put forward, with turbulent kinetic energy and dissipation supplied by an allied turbulence model. A number of flow cases, challenging for conventional RANS methods, are investigated; results show that the shock-turbulent boundary layer is captured in a much more convincing way by the gas-kinetic scheme.