paper

Enhanced Wall Boundary Modeling for Turbulent Flows Using the Lattice Boltzmann Method with Adaptive Cartesian Grids

arXiv:2601.18443 · doi:10.1063/5.0306421

Abstract

We propose an enhanced wall-boundary treatment for the lattice Boltzmann method (LBM), designed for high-Reynolds-number turbulent flows on adaptively refined Cartesian grids. The method improves the slip-velocity bounce-back scheme by coupling it with a near-wall turbulence model based on an analytical wall function. The Spalart-Allmaras (negative) turbulence model is solved using a second-order finite-difference scheme and integrated within the LBM framework to statistically represent the Reynolds-Averaged Navier-Stokes (RANS) equations (LBM-RANS). The approach is validated on two benchmark configurations: the National Advisory Committee for Aeronautics (NACA) 0012 airfoil and the McDonnell Douglas (MD)-30P30N multi-element high-lift configuration. LBM-RANS results show good agreement with conventional finite-volume RANS solutions and experimental data for key aerodynamic quantities, including pressure and skin-friction distributions, as well as turbulent boundary layer velocity profiles and eddy-viscosity fields. The method delivers smooth and accurate predictions of skin friction, which are often challenging for immersed-boundary approaches on Cartesian grids. The auxiliary geometric data required for enforcing the turbulent boundary condition are minimal, making the method potentially well-suited for graphics processing unit (GPU)-based implementations. Moreover, no ad-hoc near-wall treatments are needed, as the boundary condition is applied naturally via the link-wise bounce-back scheme. These results illustrate that the proposed LBM-RANS framework can robustly and accurately simulate high-Reynolds-number turbulent two-dimensional (2D) flows over complex aerodynamic geometries under equilibrium or near-equilibrium conditions.

57 pages. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Physics of Fluids 1 January 2026; 38 (1): 015169, https://doi.org/10.1063/5.0306421 and may be found at https://pubs.aip.org/aip/pof/article/38/1/015169/3378074/Enhanced-wall-boundary-modeling-for-turbulent

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