From automata to fluid flow: Comparisons of simulation and theory

Lattice-gas automata have been proposed as a new way of doing numerical calculations for hydrodynamic systems. Here, a lattice-gas simulation is run to see whether its behavior really does correspond, as proposed, to that of the Navier-Stokes equation. The geometry used is the two-dimensional version of laminar pipe flow. Three checks on the existing theory are performed. The parabolic profile of momentum density arising from the dynamics is quantitatively verified. So is the equation of state, which arises from the statistical mechanics of the system. Finally, the well-known logarithmic divergence in the viscosity is observed in the automaton and is shown to disagree with the earliest theoretical predictions in this system. Proper agreement is achieved, however, when the theory is extended to include three extra (recently discovered) conserved quantities. In this way, checks of both linear and nonlinear parts of the hydrodynamic description of lattice-gas automata have been achieved.