The effect of lattice models within the lattice Boltzmann method in the simulation of wall-bounded turbulent flows

This study investigated the effect of 3D lattice models (D3Q19 and D3Q27 lattices) on the simulation results of wall-bounded turbulent flows in a circular pipe and in a square duct. The LES with the Smagorinsky subgrid-scale (SGS) model was adopted for the turbulence simulation. To improve the credibility of our results on the lattice model effect, a comprehensive sensitivity study was performed of boundary treatment techniques and collision models, as well as grid sizes in the simulation of the turbulent pipe flows. Through the turbulent circular pipe flow simulation, it was discovered that the D3Q27 lattice model could achieve the rotational invariance in terms of long-time-averaged turbulence statistics and generated the results comparable to the DNS data, while the D3Q19 lattice model broke the rotational invariance and produced unreasonable data. In the turbulent square duct flow simulation, the rotational invariance was evaluated by comparing the results before and after rotating the geometry by 45° about a center. As in the circular pipe flow simulation, the D3Q19 lattice model could not achieve the rotational invariance while the D3Q27 lattice model could. The D3Q19 lattice model also produced poor results compared to those from the D3Q27 lattice model. These defects of the D3Q19 lattice model could be explained by the planes consisting of 2D lattices with five velocities (called defective planes in this study) in the D3Q19 lattice model, based on White and Chong’s [14] hypothesis. The defective planes had a deficiency in the momentum transfer of flow and turbulence, thus breaking the rotational invariance and causing the inaccurate results for tested problems.