Cellular automaton formulation of passive scalar dynamics

Abstract
Cellular automata modeling of the advection of a passive scalar in a two‐dimensional flow is examined in the context of discrete lattice kinetic theory. It is shown that if the passive scalar is represented by tagging or ‘‘coloring’’ automation particles a passive advection–diffusion equation emerges without use of perturbation expansions. For the specific case of the hydrodynamic lattice gas model of Frisch, Hasslacher, and Pomeau [Phys. Rev. Lett. 5 6, 1505 (1986)] the diffusion coefficient is calculated by perturbation.