Lattice Boltzmann simulation of cavity flows at various Reynolds numbers

Abstract

The lattice Boltzmann method (LBM) is a numerical method evolved from the statistical approach that has been well-accepted as an alternative numerical scheme for computational fluid dynamics (CFD). In comparison to other numerical schemes, the lattice Boltzmann method (LBM) can be regarded as a "bottom-up" approach that derives the Navier-Stokes equation through statistical behavior of particle dynamics. Hence, this paper presents the simulation of lid-driven cavity for deep and shallow flow using the lattice Boltzmann method where the effect of the Reynolds number on the flow pattern at aspect ratios of 0.25, 0.5, 1.5 and 4.0 was studied. These types of flow exhibit a number of interesting physical features but are scarcely simulated using the LBM scheme. The source code was established based on the BGK model on rectangular lattice geometry. The comparison of the results was in excellent agreement with those gathered from the literature even with relatively coarse grids applied to the numerical calculation.