Application of Lattice Boltzmann Method (LBM) for Unidirectional Problems in Fluid Mechanics

Lattice Boltzmann method (LBM) is a relatively new simulation technique for complex fluid systemsand has attracted many interest from researches in the computational physics. Due to its particulate natureand local dynamics, LBM has several advantages over other conventional computational fluid dynamics(CFD) methods, especially in dealing with complex boundaries, incorporating microscopic interactions,and parallelization of the algorithm.In this study, we have applied LBM on Couette flow and face with this modern approach rather thanconventional one. This is so fastidious and simplest method compared with the previous ones. Thenumerical results are presented in the form of diagrams and contours. We represent our numerical resultsin the form of diagrams and contour, which illustrates them very well. We will represent 100 lattice in bothx- and y-directions and will examine the effect of elapsed time, kinematic viscosity, and time step on oursolution. We will show that because of our infinity slab in x-direction (  x  0 ), velocity profile in ydirectionwill not vary. This is the fundamental assumption of unidirectional flows. We will also depictvelocity profile, too, which takes a parabolic configuration when we consider its variation with respect tox-direction. Once we will drown the velocity diagram versus length, we will also discuss on its steep, too.This consideration will show that shear stress will decrease with respect to time along x-direction. At theend thought, we will show that increasing of kinematic viscosity must have a same effect as increasing ofelapsed time, where time step has nothing to do with this Velocity distribution.

Keywords:

Lattice Boltzmann method (LBM) , Couette flow , Distribution function , Particles arrangements , Diffusion equation