Three-dimensional lattice gas with minimal interactions

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Abstract
An interaction has been added to the classical lattice gas model that exchanges momentum between sites. The hydrodynamic limit of the model can be obtained from a Chapman-Enskog expansion and all the coefficients can be expressed explicitly. The interaction contributions to viscous terms are independent of the initial interaction-free model and grow like r2. When the interaction range r is large enough, the pressure acquires a negative slope for certain densities. The model then has a phase transition, observed in simulations. Some examples of a three-dimensional phase separation are shown. Whatever the dimension of space, the model can be represented by a cellular automaton with only nearest neighbor communications, using messenger particles or photons. In 2 dimensions of space, this allows fitting the model into a 16 bit table adequate for a special purpose cellular automaton machine like the RAP1.

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