A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part II: Extension towards turbulent flow simulation

Abstract

In this paper, the finite volume lattice Boltzmann method (FVLBM) on unstructured grid presented in Part I of this paper is extended to simulate the turbulent flows. To model the turbulent effect, the $k-\omega$ SST turbulence model is incorporated into the present FVLBM framework and also is solved by the finite volume method. Based on the eddy viscosity hypothesis, the eddy viscosity is computed from the solution of k-\omega SST model, and the total viscosity is modified by adding this eddy viscosity to the laminar (kinematic) viscosity given in the Bhatnagar-Gross-Krook collision term. In order to enhance the computational efficiency, the three-stage second-order implicit-explicit (IMEX) Runge-Kutta method is used for temporal discretization and the time step can be larger one- or two-order of magnitude compared with explicit Euler forward scheme. Though the computational cost is increased, the finial computational efficiency is enhanced about one-order of magnitude and the good results also can be obtained at large time step through the test case of lid-driven cavity flow. Two turbulent flow cases are carried out to validate the present method, including flow over backward-facing step and flow around NACA0012 airfoil. Our numerical results are found to be in agreement with experimental data and numerical solutions, demonstrating applicability of the present FVLBM coupled with k-\omega SST model to accurately predict the incompressible turbulent flows.