Theory and application of lattice Boltzmann numerical method on isothermal fluid flow problem

Abstract

Lattice Boltzmann method (LBM), a numerical model based on the physical at the mesoscopic scale, has received much attention since the 1980’s due to its simplicity and easy implementation. Due to their ability to incorporate particle interactions at the mesoscopic level, LB models fit for simulating the behavior of complex flow system. It has also been proven to be a useful tool for solving a wide range of complex flows, such as turbulent (Jonas et al., 2006), flow inside porous media (Chen and Doolen, 1998), immiscible fluid (Halliday and Care, 1996), magnetohydrodynamics (Breyiannis and Valougeorgis, 2004), and many others. In this paper, we will consider a BGK lattice Boltzmann model (Bhatnagar et al., 1954) for single isothermal fluid flow system. Two-dimensional lid-driven cavity flow at various Reynolds numbers is solved. Comparisons in terms of vortex behavior and distribution of velocity components inside the cavity are presented. The objective of this paper is to demonstrate the capability of lattice Boltzmann BGK method and to stimulate further studies using the lattice Boltzmann approach.