Numerical Simulation Of Overhead-driven Flow Based On The Lattice Boltzmann Method

Partial differential equations and their applications play a crucial role in related fields such as mathematics and physics.With the rapid development of modern computer technology,more and more methods for solving nonlinear partial differential equation have been developed.Among them,the emerging Lattice Boltzmann method(LBM)is a numerical method that simulates the macroscopic behavior of fluids from a mesoscopic perspective by solving Boltzmann equations,using fully discrete dynamic models in both time and space.The main work of this study,based on previous research,is as follows:1、Introduced the development history,basic theories,and basic models of LBM.And using Taylor expansion and Chapman-Enskog multi-scale expansion techniques,the basic model was restored to the standard incompressible NavierStokes equation,and the specific solution process was provided.2、For the boundary treatment of LBM,this article adopts a non equilibrium extrapolation format and provides detailed derivation explanations.3、This study conducted numerical simulations based on this method for the driving flow problem of the top cover square cavity,and discussed the simulation results.And small perturbations were made to the initial conditions,and robustness analysis was conducted.By comparing with existing experimental and numerical research results,the correctness,accuracy,and stability of using LBM to simulate the driving flow of the top cover square cavity have been verified.