A Modified Gas-Kinetic Scheme for Turbulent Flow (Communications in Computational Physics, 2014)
The implementation of a turbulent gas-kinetic scheme into a finite-volumeRANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave anda turbulent boundary layer, where the shock-turbulent boundary layer is captured in amuch more convincing way than it normally is by conventional schemes based on theNavier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is partof the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained intoa linear relation with the strain rate. Instead, it is modeled on the basis of the analogybetween particles and eddies, without any assumptions on the type of turbulence orflow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolvedto resolved scales – very much like a degree of rarefaction – is not taken into accounteven if it may grow to non-negligible values in flow regions such as shocklayers. It isprecisely in these flow regions, that the turbulent gas-kinetic scheme seems to providemore accurate predictions than conventional schemes.