Journal of Statistical Physics, Vol. 65, Nos. 1/2, 1991. p. 97-138.
A new cellular-automaton model for fluid dynamics is introduced. Unlike the conventional FHP-type models, the model uses easily implementable, deterministic pair interaction rules which work on arbitrary-dimensional orthogonal lattices. The statistical and hydrodynamic theory of the model is developed, and the Navier-Stokes-like hydrodynamic equations that describe the macroscopic behavior of the model are derived. It turns out that the unwanted anisotropic convection behavior can be eliminated in the incompressible limit by suitable choice of the mass density. An explicit expression for the viscosity tensor is calculated from a Boltzmann-type approximation. Unfortunately, the viscosity turns out to be anisotropic, which is a drawback as against the conventional FHP and FCHC models. Nevertheless, the new model could become interesting for fluid dynamic problems with additional variables (e.g., free surfaces), especially in two dimensions, since its simple rules could relatively easily be extended for such cases.