  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.
