A gas-kinetic scheme coupled with SST model for turbulent flows

In order to simulate the compressible and incompressible turbulent flows, a gas-kinetic scheme (GKS) based on the Bhatnagar–Gross–Krook (BGK) model coupled with the shear stress transport (SST) two-equation turbulence model is developed. The SST model is a two-equation eddy-viscosity model based on the k−ω and k−ε models, which is one of the most common turbulence models and widely used in Reynolds averaged Navier–Stokes (RANS) modeling for turbulent flows. In this study, we implement GKS–SST coupling model by (a) solving the GKS and SST models in vertex-based finite volume method on hybrid grids; (b) incorporating the SST model into the GKS based on the eddy viscosity hypothesis and using the eddy viscosity to modify the collision time in gas-kinetic scheme; (c) using a modified Venkatakrishnan limiter for hybrid and highly stretched grids during the initial reconstruction stage; (d) applying the boundary conditions adopted from vertex-based solvers for Navier–Stokes equations in present GKS solver. The original gas-kinetic scheme has been proved to be an accurate and effective approach for incompressible and compressible laminar flows, and the SST turbulence model is incorporated here for the turbulent flow. The eddy viscosity at the cell centers is obtained by solving SST model, and then the eddy viscosity on the cell interface can be interpolated from cell centers around. Numerical experiments performed on high Reynolds number turbulent flows around the 2D zero pressure gradient flat plate and a RAE2822 airfoil demonstrate the applicability of the GKS–SST model presented in this study for simulations of high Reynolds number turbulent flows.