Hydrodynamics of lattice-gas automata

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Abstract
The linear and nonlinear hydrodynamics of the two-dimensional lattice-gas automata (LGA) are discussed. The physics of the LGA is found to be richer than previously expected. Together with sound and shear waves (characteristic of simple fluids) there are three new hydrodynamic modes. The conserved quantities corresponding to the latter arise from a feature of the microscopic definition of the LGA; i.e., the particles of the microscopic gas occupy the sites of a regular lattice and can only hop from one site to its nearest neighbors. The presence of these new conserved quantities has unexpected results on the macroscopic behavior of the fluid. In fact, there is a nonlinear coupling between the two classes of modes, and while the new conserved densities are merely convected by the momentum density, the current of the latter contains terms that depend only on the new modes. Thus the presence of a finite amount of the new conserved densities produces flow patterns that are not solutions of the Navier-Stokes equation. Although only the two-dimensional hexagonal-lattice gas is discussed, the arguments described here apply with equal force to currently proposed three-dimensional models.