A Poiseuille Viscometer for Lattice Gas Automata.

Abstract

Ab stra ct. Lattice gas automata have been recently proposed as a new technique for the numerical integration of the two-dimensional Nav ier-Stokes equation. We have accurately tes ted a stra ightforward var iant of the original model, due to Fr isch, Hasslacher, and Pomeau, in a simp le geometry equivalent to two-dimensional Poiseuille (Chan-nel) flow dr iven by a uniform body force. The momentum density profile produced by this simulation agrees well with the pa rabolic pro file predicted by the macroscopic descrip-t ion of the gas given by Frisch et al. We have used the simulated flow to compute t he shea r viscosity of the lat tice gas and have found ag reement with the results obtained by d 'Humieres et al. 110] using shear wave re laxation measurements, and, in t he low density limit, with theoretica l predictions obtained from the Boltzmann description of the gas [171. 1. lutroduction In a now classic paper, Frisch, Hasslacher, and Pomeau [1] proposed a new te chnique for solving t he two-dimensional Navier-Stokes equat ion based on the implementat ion of a lattice gas automaton. Their original idea has rece nt ly been extended to two-dimens ional binary fluids, two-dimensional magnetohydrodynamics, three-dimensional Navier-Stokes, and ot her inter-est ing problems [41. Two-dimensional lat t ice gas ·automata have been described in great de-ta il in reference 3. We will therefore give only a very shor t descript ion of the model in order to define the nomenclature used. Lat tice gas automata are based on the construction of an idealized mi-croscopic world of par ticl es living on a lat t ice. The part icles can move on the lattice by "hopping " from site to site. In the specific examples consid-ered in this pape r, we allow only hops from a site to its nearest neighbors (a particl e may also remain stationary at its current site) and we ind icate t hese moti ons with the vectors Ca. The COl are traditionally interpreted