Application of Lattice Boltzmann Method to Simulation of Compressible Turbulent Flow

The main goal of this paper is to develop the coupled double-distribution-function (DDF) lattice Boltzmann method (LBM) for simulation of subsonic and transonic turbulent flows. In the present study, we adopt the second-order implicit-explicit (IMEX) Runge-Kutta schemes for time discretization and the Non-Oscillatory and Non-Free-Parameters Dissipative (NND) finite difference scheme for space discretization. The Sutherland's law is used for expressing the viscosity of the fluid due to considerable temperature change. Also, the Spalart-Allmaras (SA) turbulence model is incorporated in order for the turbulent flow effect to be pronounced. Numerical experiments are performed on different turbulent compressible flows around a NACA0012 airfoil with body-fitted grid. Our numerical results are found to be in good agreement with experiment data and/or other numerical solutions, demonstrating the applicability of the method presented in this study to simulations of both subsonic and transonic turbulent flows.