Analysis of the Lattice Boltzmann Equation

Abstract

After reading this chapter, you will be familiar with many in-depth aspects of the lattice Boltzmann method. You will have a detailed understanding of how the Chapman-Enskog analysis can be used to determine how the lattice Boltzmann equation and its variations behave on the macroscopic Navier-Stokes level. You will know a number of such variations that result in different macroscopic behaviour from the standard lattice Boltzmann equation. Necessary and sufficient conditions that serve as stability guidelines for lattice Boltzmann simulations will be known to you, along with how to improve the stability of a given simulation. You will also have insight into the accuracy of both general simulations and lattice Boltzmann simulations. For the latter, you will understand what the sources of inaccuracy are, and how they may be reduced or nullified.