On the derivations of lattice Boltzmann evolution equation

Abstract

A comparative analysis on the popular schemes for evaluating evolution equation in lattice Boltzmann method (LBM) is presented in this paper. It includes two classical characteristic-line schemes, Boesh-Karlin and He-Luo scheme, and a author-proposed scheme, Taylor-expansion scheme, originating from the extension of He-Luo scheme. We detailly discuss the mathematical mechanism and the equilibrium distribution evolution behind them. By analyzing the conflict between prediction and derivation, we address the preconditions for these schemes. At the end, we conclude their pros and cons and suggest scheme's applicable scene based on their derivation procedure and further development capacity.