Lattice Boltzmann Method Based on 3D Orthogonal Curvilinear Coordinates for Effective Simulation of Turbulent Shear Flows

Turbulent shear flows bounded by walls are inherently multiscale and 3D, and the use of variable grids that follow the flow features is essential for efficient simulations. However, the lattice Boltzmann (LB) methods generally use uniform Cartesian grids with high computational requirements. We present a new formulation of the LB method for the Navier-Stokes (NS) equations based on 3D orthogonal curvilinear coordinates (OCC) to perform eddy-capturing simulations more effectively via variable grids. We construct the collision step via a Chapman-Enskog analysis such that the relaxations of various moments to their equilibria as well as the body forces are based on the local metric factors and their spatial derivatives that parametrize the grid variations and recovers the 3D NS equations consistently. The new algorithm maintains simplicity of the standard collide-and-stream steps of the usual LB approach while allowing continuously variable grids, and is implemented using our recently developed Fokker-Planck collision model based on central moments for improved stability and including subgrid scale turbulence model expressed in OCC. We report the results of parallel simulations using this 3D OCC-LB method for various canonical wall-bounded turbulent shear flows.