Wall boundary conditions for Lattice Boltzmann simulations of turbulent flows with wall functions

TL;DR

This study compares two wall boundary condition schemes for Lattice Boltzmann simulations of turbulent flows with wall functions, highlighting the robustness of slip-velocity bounce-back and the sensitivity of regularized approaches to wall-normal velocity gradients.

Contribution

It introduces and evaluates a hybrid regularized boundary scheme and compares its performance with the slip-velocity bounce-back method in turbulent flow simulations.

Findings

Slip-velocity bounce-back is consistent in accuracy and mesh convergence.

Regularized boundary schemes are highly sensitive to wall-normal velocity gradient reconstruction.

A hybrid scheme with calibrated gradient reconstruction is proposed for further investigation.

Abstract

This paper investigates wall boundary condition schemes for the simulation of turbulent flows using the Lattice Boltzmann method (LBM) coupled to turbulence models with wall functions. The analysis focuses on two schemes: a regularized boundary scheme with third-order reconstruction of the velocity gradients using wall function data and a slip-velocity bounce-back scheme. The LBM solver is coupled to the Spalart-Allmaras turbulence model and uses a model consistent wall function. The performance of the wall boundary schemes is assessed in 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 treatments on turbulence modeling. The analysis shows that, for the selected test cases, the slip-velocity bounce-back approach, which has received relatively little attention within the context of LBM coupled to Reynolds-Averaged Navier-Stokes (RANS) turbulence models with wall functions, behaves fairly consistently in terms of both accuracy and mesh convergence. The regularized-based approach, on the other hand, appears 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 of the regularized boundary schemes on near-wall gradients, which had been noted before in the literature, requires the use of ad-hoc gradient reconstruction techniques, requirements that are not present in the slip-velocity bounce-back method. A hybrid regularized boundary scheme that blends two different gradient reconstruction techniques but requires calibration is introduced as a tool to investigate this effect.