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

TL;DR

This paper introduces an improved wall boundary treatment for the lattice Boltzmann method, coupling it with a turbulence model to accurately simulate high-Reynolds-number turbulent flows on adaptive Cartesian grids, validated on aerodynamic benchmarks.

Contribution

It develops a novel LBM-RANS approach with enhanced boundary conditions and minimal geometric data, enabling accurate turbulent flow simulations on complex geometries.

Findings

Good agreement with experimental data and finite-volume RANS solutions.

Accurate predictions of skin friction and boundary layer profiles.

Method is suitable for GPU implementation and complex geometries.

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.