Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases

In this, paper a procedure for systematic a priori derivation of the lattic e Boltzmann models for nonideal gases from the Enskog equation (the modifie d Boltzmann equation for dense gases) is presented. This treatment provides a unified theory of lattice Boltzmann models for nonideal gases. The latti ce Boltzmann equation is systematically obtained by discretizing the Enskog equation in phase space and time. The lattice Boltzmann model derived in t his paper is thermodynamically consistent up to the order of discretization error. Existing lattice Boltzmann models for nonideal gases are analyzed a nd compared in detail. An evaluation of these models is made in light of th e general procedure to construct the lattice Boltzmann model for nonideal g ases presented in this work.