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 $k-\omega$ 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 $k-\omega$ 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. 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 $k-\omega$ SST model to accurately predict the incompressible turbulent flows.

在本文中，对非结构化网格（这些论文的第一部分）上的原始有限体积格子玻尔兹曼方法（FVLBM）进行了扩展，以模拟湍流。为了模拟湍流效应，$ķ-\omega$SST湍流模型被合并到当前的FVLBM框架中，并且也通过有限体积法求解。基于涡流粘度假设，由$ķ-\omega$SST模型，通过将涡流粘度添加到Bhatnagar–Gross–Krook碰撞项中给出的层流（运动）粘度中来修改总粘度。由于在原始FVLBM方案中使用显式方法解决了碰撞项，因此模拟高雷诺数流的计算效率要低得多。这是由于以下事实：由碰撞项的稳定性条件决定的最大时间步长（小于松弛时间的两倍）比由CFL条件决定的最大时间步长要小得多。为了提高计算效率，将三阶段二阶隐式-显式（IMEX）Runge-Kutta方法用于时间离散化，并且时间步长可以比显式欧拉大一到两个数量级。前向方案。尽管增加了计算成本，但最终计算效率却提高了大约一个数量级，并且通过盖驱动型腔流的测试案例，还可以在较大的时间步长上获得良好的结果。进行了两个湍流情况以验证本方法，包括在向后步骤上方的流动和围绕NACA0012机翼的流动。数值结果与实验数据和数值解吻合，证明了本FVLBM结合了FVLBM的适用性。包括在向后的台阶上流动以及在NACA0012机翼周围流动。数值结果与实验数据和数值解吻合，证明了本FVLBM结合了FVLBM的适用性。包括在向后的台阶上流动以及在NACA0012机翼周围流动。数值结果与实验数据和数值解吻合，证明了本FVLBM结合了FVLBM的适用性。$ķ-\omega$ SST模型可准确预测不可压缩的湍流。