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

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