Application of Taylor series expansion and Least-squares-based lattice Boltzmann method to simulate turbulent flows

Lattice Boltzmann method (LBM) has become an alternative method of computing a variety of fluid flows, ranging from low Reynolds number laminar flows to highly turbulent flows. For turbulent flows, non-uniform grids are preferred. Taylor series expansion- and least-squares-based LBM (TLLBM) is an effective and convenient way to extend standard LBM to be used on arbitrary meshes. In order to show its ability to solve turbulent flows, we combine it with k–ω and S-A turbulence models. To validate these combinations, the benchmark problems of the turbulent channel flow and the turbulent flow over a backward facing step at Re = 44 000 are simulated. Our results compare well with the analytical solution and the experimental results of Kim et al. [22]. This shows that the combination of TLLBM with turbulence model can solve turbulent flows effectively.