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 original finite volume lattice Boltzmann method (FVLBM) on an unstructured grid (Part I of these twin papers) is extended to simulate turbulent flows. To model the turbulent effect, the k − ω SST turbulence model is incorporated into the present FVLBM framework and is also solved by the finite volume method. Based on the eddy viscosity hypothesis, the eddy viscosity is computed from the solution of the k − ω 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. Because of solving for the collision term with the explicit method in the original FVLBM scheme, the computational efficiency is much lower for simulating high Reynolds number flow. This is due to the fact that the largest time step decided by the stability condition of the collision term, which is less than twice the relaxation time, is much smaller than that decided by the CFL condition. 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 one or two orders of magnitude larger as compared with the explicit Euler forward scheme. Although the computational cost is increased, the final computational efficiency is enhanced by about one-order of magnitude and good results can also be obtained at a large time step through the test case of a lid-driven cavity flow. Two turbulent flow cases are carried out to validate the present method, including flow over a backward-facing step and flow around a NACA0012 airfoil. The numerical results are found to be in agreement with experimental data and numerical solutions, demonstrating the applicability of the present FVLBM coupled with the k − ω SST model to accurately predict the incompressible turbulent flows.