Unified Theory of Lattice Boltzmann Models for Nonideal Gases

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Abstract
A nonideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for nonideal gases. The existing lattice Boltzmann models for nonideal gases are analyzed and compared with the model derived here.