Complex Systems

A Poiseuille Viscometer for Lattice Gas Automata Download PDF

Leo P. Kadanoff
Guy R. McNamara
Gianluigi Zanetti
The Enrico Fermi and James Franck Institutes, The University of Chicago,
5640 South Ellis Avenue, Chicago, IL 60637, USA


Lattice gas automata have been recently proposed as a new technique for the numerical integration of the two-dimensional Navier-Stokes equation. We have accurately tested a straightforward variant of the original model, due to Frisch, Hasslacher, and Pomeau, in a simple geometry equivalent to two-dimensional Poiseuille (Channel) flow driven by a uniform body force.

The momentum density profile produced by this simulation agrees well with the parabolic profile predicted by the macroscopic description of the gas given by Frisch et al. We have used the simulated flow to compute the shear viscosity of the lattice gas and have found agreement with the results obtained by d'Humiéres et al. [10] using shear wave relaxation measurements, and, in the low density limit, with theoretical predictions obtained from the Boltzmann description of the gas [17].