Theoretical framework: from Boltzmann to BGK
Introduction to the Lattice Boltzmann Method for Fluid Mechanics

Boltzmann's theory was developed within the framework of the assumptions of the kinetic theory of gases. It applies to dilute gases, i.e. gases for which the mean free path of the molecules is greater than the interaction distance between the molecules. We will see later that the LBM method can be applied far beyond this framework.

Furthermore, the gas under consideration has only one type of molecule, and collisions between these molecules are elastic. Kinetic energy is thus conserved during collisions.

The theoretical framework of kinetic gas theory and the Boltzmann equation, as well as subsequent developments, cover a much wider range of applications than simply the numerical resolution of fluid flows. Readers are referred in particular to the articles on the properties of gases