Lattice-Gas Automata for Numerical Experimental Verification of Maxwell-Boltzmann Distribution

Abstract

Lattice-gas automata model has been applied to simulate the distribution function of gas molecules. This study shows a transition of a single-component velocity distribution from its initial non-equilibrium to its final equilibrium. The distribution is independent of time when the system reaches its equilibrium. For a sufficiently dilute gas in equilibrium, the distribution function of x-velocity component is a Maxwell-Boltzmann distribution with its average velocity component is between zero and 3% of its maximum value.
This numerical experiment also obtained that the speed distribution for two-dimensional problem is a Maxwell-Boltzmann distribution. From 12 trials, average and root mean square speeds are (8.6±0.3) and (9.7±0.3) lattice units per time step respectively. We introduce a factor β to converse the unit of speed to be in meter per second. Therefore, the absolute temperature (in Kelvin) of the experiment is expressed in the mass of one molecule and Boltzmann constant as (47,1±3,2)β2 m/k.