Traction-Consistent Wall Boundary Formulation for Turbulent Lattice–Boltzmann Simulations
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Accurate enforcement of near-wall momentum transfer is a major challenge for wall-modeled Large-Eddy simulations (WMLES) of turbulent flows using the Lattice--Boltzmann method (LBM). Conventional LBM wall treatments are commonly formulated in terms of prescribed velocities or bounce-back–type schemes, in which the resulting wall shear stress emerges implicitly from numerical gradients. When coupled with wall models, such approaches may lead to grid-dependent behavior and inconsistencies in global momentum balance. In this work, we investigate a momentum-consistent boundary framework, compatible with wall-modeled large-eddy simulation, for enforcing wall shear stress in LBM simulations of turbulent wall-bounded flows. The proposed approach aims to directly match the traction predicted by a wall model through a traction-based boundary formulation with the momentum exchange at the fluid–solid interface, without relying on near-wall velocity resolution. This consistency can be achieved either by reconstructing the non-equilibrium momentum flux tensor at wall-adjacent fluid nodes or, alternatively, by inferring a boundary velocity that yields the target shear force through the LBM momentum exchange mechanism. Both formulations are compatible with regularized collision operators and compressible LBM formulations. The wall shear stress is supplied by an external wall model and imposed in a manner that decouples near-wall momentum transfer from numerical viscosity and grid spacing, resulting in a momentum-consistent discretization of the wall boundary. The framework is compatible with subgrid-scale turbulence models and naturally accommodates vanishing eddy viscosity in the vicinity of solid boundaries. The proposed boundary treatment is assessed using a set of canonical wall-bounded flow configurations representative of turbulent internal flows. The results demonstrate stable behavior and physically consistent momentum transfer without requiring fine near-wall resolution, indicating the suitability of the method for wall-modeled LBM simulations at high Reynolds numbers.
