Research On Lattice Boltzmann Method And Application

The present thesis covers two main parts: the theoretical research of Lattice Boltzmann Method, and application of LBM in engineering—flow in a 2-D lid driven cavity, flow around a circular cylinder, and flow simulation around airfoil and analysis of the final results. After systematically introducing the origination, development and current situation of LBM, the physical and theoretical knowledge is described and mathematical representation of the standard LBM and the relationship between Lattice Boltzmann Equation and macroscopic Navier-Stokes equations is introduced. Moreover, the two dimensional particle velocity models of LBM are described in detail. In order to improve the application of LBM in engineering, non-uniform grid could be used in the simulation. Some recent methods are shown. Based on the above description, a new version of LBM using non-uniform grid is proposed and the deriving process is presented in detail. In addition, incompressible model for the LBM and some boundary conditions are discussed. Finally, by using this new method, flow in a 2-D lid driven cavity, flow around a circular cylinder, and flow simulation around NACA0012 airfoil with different Reynolds numbers are performed. The careful analysis and comparison are finished, which shows that the new method is efficient and robust.