Towards the simplest hydrodynamic lattice-gas model

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier–Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman–Enskog analysis to determine the form of the Navier–Stokes equations