A wall function approach in lattice Boltzmann method: algorithm and validation using turbulent channel flow

In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, which corresponds to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when addressing high Reynolds number flows using coarse-grid systems. In this study, we proposed a "wall-function bounce (WFB)" boundary that incorporates a wall function into the LBM's boundary condition and overcomes the limitation of the BB. The WFB boundary calculates the appropriate shear drag on the wall using a wall function model, and thereafter modifies distribution functions to reflect the shear drag. The Spalding's law was utilized as the wall function in WFB. Simulations of turbulent channel flow at $Re_{\tau}$=640 and 2003 using the LBM-based large-eddy simulation (LBM-LES) were conducted to validate the effectiveness of the proposed boundary condition. The results indicate that the BB boundary underestimated the time-averaged velocity in the buffer layer at $Re_{\tau}$=640, and the averaged velocity in the entire domain at $Re_{\tau}$=2003, when using coarse-grid systems. However, WFB obtained the proper shear drag on the wall and thus, compensated for the underestimation and agreed better with the experimental or DNS data, especially at the first-layer grid. In addition, WFB improved the Reynolds normal stress in the near-wall region to some extent. The distributions of shear stress on the wall by WFB was analogous to those by the wall model function in the finite volume method.