Lattice Boltzmann Method for Fluid Simulations

In the last two decades, the Lattice Boltzmann method (LBM) has emerged as a promising tool for modelling the Navier-Stokes equations and simulating complex fluid flows. LBM is based on microscopic models and mesoscopic kinetic equations. In some perspective, it can be viewed as a finite difference method for solving the Boltzmann transport equation. Moreover the Navier-Stokes equations can be recovered by LBM with a proper choice of the collision operator. In Section 2 and 3, we first introduce this method and describe some commonly used boundary conditions. In Section 4, the validity of this method is confirmed by comparing the numerical solution to the exact solution of the steady plane Poiseuille flow and convergence of solution is established. Some interesting numerical simulations, including the lid-driven cavity flow, flow past a circular cylinder and the Rayleigh-Bénard convection for a range of Reynolds numbers, are carried out in Section 5, 6 and 7. In Section 8, we briefly highlight the procedure of recovering the Navier-Stokes equations from LBM. A summary is provided in Section 9.