Lattice Boltzmann wall boundary conditions for RANS-based simulations with wall functions

Abstract: In this study, we investigate wall boundary condition schemes for Lattice Boltzmann simulations of turbulent flows modeled using RANS equations with wall functions. Two alternative schemes are formulated and assessed: a hybrid regularized boundary condition and a slip-velocity bounce-back scheme. Their performance is evaluated using two canonical turbulent flow cases, a fully developed channel flow and a zero-pressure-gradient flat plate boundary layer (BL), selected specifically to isolate and analyze the impact of wall boundary condition treatments on turbulence modeling. The comparative analysis reveals that the slip-velocity bounce-back approach, which has received relatively little attention within the context of LBM-RANS with wall functions, consistently outperforms the regularized-based method in terms of both accuracy and sensitivity to mesh resolution. Moreover, the regularized-based approach is shown to be highly sensitive to the reconstruction of the wall-normal velocity gradient, even in simple geometries such as flat walls where no interpolation is required. This dependency necessitates the use of specialized, ad-hoc gradient reconstruction techniques, requirements that are not present in the slip-velocity bounce-back method.