Lattice Boltzmann Theory And Its Applied Research In Fluid Dynamics

Based on Boltzmann equation, the Lattice Boltzmann Method (LBM) is a developing computational method of simulation of fluid flow recently. The traditional method of computational fluid dynamics is a discrete macroscopic continuity equation, while the lattice Boltzmann method is based on statistical physics to describe microscopic particles action to reflect the macroscopic fluid motion in a very simple way; so LBM method is simple for computation and good at dealing with complex boundaries, parallel computing, and many other advantages. Lattice Boltzmann method has been becoming a useful tool of simulation of complex physical phenomena.Although LBM has been developed rapidly and simulated fluid dynamics successfully, including homogeneous incompressible turbulence and multiphase flow in porous media. However, there are many questions worthy of study, such as incompressible thermal lattice Boltzmann model. For developing the applications of LBM, this paper made some research on dealing with moving boundary with LBM and has made numerical simulation of oscillatory flow around a cylinder and Rayleigh Benard problem. The main work and results are:(1) In consideration of the density variable, the D2Q9 model is improved, and a new equilibrium distribution function is derivates; according to the multi-component DDF-LBE model proposed by Shan, a modified D2Q9 double distribution lattice Boltzmann model is advanced;(2) According to the modified D2Q9 model, this paper simulated flow around square cylinders numerically in two directions. First, we simulated flow around a square cylinder numerically and observed the wake change of square cylinder at different Reynolds number, the results showed that:when Reynolds number is small, there are two symmetrical vortex square behind the cylinder, but there is no effect far away from the cylinder; as the Reynolds number increases, the vortex behind the square cylinder gradually broke the symmetry and changed variably, the large vortex was far away from the square cylinder, and there was a new vortex near the low wall far away from the cylinder, and as the Reynolds number bigger, the vortex was stronger, however there was no trend to spread elsewhere. We also calculated the Strouhal number as Reynolds number changed and compared with other reference, the results were consistent; Second, we simulated the flow around two paratactic square cylinders, the results showed:When the distance was small, there would be a vortex behind each cylinder, the drag coefficient and lift coefficient were not the same; as the distance increasing, there would be a vortex behind each cylinders, and there was another vortex far away from the first vortex upper(lower) behind the square cylinder, and the drag coefficient and lift coefficient were mean the same; with the growing distance between the two cylinders gradually, the drift flow began, there was a vortex behind each square cylinder, and there was another vortex far away from the first vortex behind the square cylinder; it was like a 2D Poiseuille flow between the two cylinders; as the distance increases further, the drift flow weaken gradually and the distance came to a criticality drift disappeared, and there were symmetrical wake behind the cylinders;(3) With the improved D2Q9 DDF-LBE model, this paper simulated Rayleigh Benard convection in a cavity. In consideration of the density variation with temperature variation, we got the convection velocity and temperature with time variation, we also got the streamlines and isothermal lines distribution; and at different Rayleigh number of cases, the relation between the average Nusselt number and Rayleigh number is obtained; compared with data the simulation results from other reference, the results are very consistent, the improved double distribution lattice Boltzmann model is proven to effective.