Regularised Lattice Boltzmann–URANS framework for bluff-body flows: Application to a square cylinder Re=200–3000

Turbulent flow past bluff bodies is computationally demanding to simulate accurately. Scale-resolving approaches such as large-eddy simulation and direct numerical simulation require fully three-dimensional domains and long simulation times, making parametric studies across a wide Reynolds number range prohibitively expensive. The unsteady Reynolds-averaged Navier–Stokes approach reduces this cost by eliminating the spanwise direction, but conventional finite-volume solvers still require iterative pressure–velocity coupling at every time step. The Lattice Boltzmann Method (LBM) offers a natural alternative since its collision and streaming operations are strictly local, no global linear systems are required, and the method maps efficiently onto data-parallel GPU hardware, making it well suited to parametric studies at multiple Reynolds numbers on a single workstation. In the present work, an LBM solver coupled with the Menter Shear Stress Transport (SST) k – ω turbulence closure is developed for flow past a stationary square cylinder at moderate Reynolds numbers ( R e = 200 –3000). The choice of collision operator is central to the performance of any LBM solver. The standard BGK scheme is unstable at the low relaxation times encountered in turbulent flows, and the multiple-relaxation-time operator, though more stable, requires matrix transformations that reduce GPU efficiency. The regularised collision operator resolves both issues by reconstructing the non-equilibrium distribution analytically from the second-order stress tensor, and is therefore adopted in the present solver. The solver is validated against established numerical and experimental benchmarks, demonstrating good agreement in time-mean drag coefficient C ¯ D , RMS lift coefficient C L , rms , and Strouhal number S t across the full Reynolds number range. The instantaneous vorticity fields and time-averaged pressure distributions reveal the systematic evolution of wake topology from a transitional von Kármán vortex street at R e = 200 to a compact turbulent near-wake with vigorous shear layer roll-up at R e = 3000 .