Scrutinizing lattice Boltzmann methods for direct numerical simulations of turbulent channel flows

Abstract

The paper reports on the predictive performance of Lattice Boltzmann methods in turbulent channel flows. Attention is confined to model-free (direct) numerical simulations at Reτ=180 using essentially different collision models, i.e. the Bhatnagar–Gross–Krook (BGK), the Multiple-Relaxation-Time (MRT) and the Cumulant model. The three approaches are assessed by a comparison of the predicted mean flow and turbulence statistics against benchmark Navier–Stokes solutions. Initial studies employ a fine isotropic grid which resolves all relevant scales. Subsequently, a sequence of four gradually decreasing resolutions is utilized to analyze the sensitivity of the collision models for an inadequate resolution. Moreover, the influence of the Mach number and the discretization on the predictive accuracy of the weakly compressible LBM framework is briefly addressed. Whilst the Mach number influence is negligible below Ma < 0.1, and the predictive agreement with reference data is generally satisfactory in conjunction with all employed discretizations for the fine grid, significant disparities between the collision models are observed when the mesh is coarsened. The BGK approach offers an improved predictive agreement with Navier–Stokes results for an adequate resolution, which comes at the expense of severe (formerly reported) stability issues that emanate from the interface between the buffer and the log-layer for an under-resolved flow. Both the MRT and the Cumulant model are more demanding with respect to grid convergence. As opposed to the BGK and the MRT model, the Cumulant model remains stable over a wide range of resolutions. The reason can be attributed to a rigid alignment between predicted streamwise two-point correlation lengths and the grid spacing, which augments the damping of sub-grid scales. The latter is deemed to be an inherent feature of the model.