Solution to navier-stokes equations for lid-driven cavity problem: comparisons between lattice boltzmann and splitting method

Abstract

Solutions to the Navier Stokes equations have been pursued by many researchers. One of the recent methods is lattice Boltzmann method, which evolves from Lattice Gas Automata, simulates fluid flows by tracking the evolution of the single particle distribution. Another method to solve fluid flow problems is by splitting the Navier Stokes equations into linear and non-linear forms, also known as splitting method. In this study, results from uniform and stretched form of splitting method are compared with results from lattice Boltzmann method. The traditional two dimensional lid driven cavity problems, with constant density, is used as the case study. For low Reynolds number transient problems, the lattice Boltzmann method requires less time as compared to that of splitting method to reach steady state conditions. As the Reynolds number increases, the lattice Boltzmann method begins to consume more time than that of splitting method. However, the lattice Boltzmann method results maintain to be the most accurate when comparisons are made with benchmark results for the same grid configuration.