Poiseuille flow and the lid-driven cavity calculate using the Lattice Boltzmann equation method

Abstract

Abstract
The aim of this article is to present the results of the lattice Boltzmann method (LBM) application as computational fluid dynamics solvers. After of short review of the basic theory and using the two-dimensional model with 9 velocities (D2Q9), the Poiseuille flow is modelled and validated the results with the analytical solutions. Also, the Lid-driven cavity is modelled and validated the results with existing data (Guía et al.). The boundary condition for static wall and moving wall are revised on the first and second model respectively. The results indicate the efficiency of LBM to simulate incompressible and laminar fluid flow. Also, that the effects of increment in the number of the lattice points, improve the computational convergence and reduce spatial oscillations of solution near geometrically singular points in the flow.