Lattice-Gas Automata For The Problem Of Kinetic Theory Of Gas During Free Expansion

The lattice-gas method has been applied to solve the problem of kinetic theory of gas in the Gay–Lussac–Joule experiment. Numerical experiments for a two-dimensional gas were carried out to determine the number of molecules in one vessel(Nr), the ratio between the mean square values of the components of molecule velocity$(\overline{v_x^2}/\overline{v_y^2})$, and the change in internal energy(ΔU)as a function of time during free expansion. These experiments were repeated for different sizes of an aperture in the partition between the two vessels.After puncturing the partition, the curve for the particle number in one vessel shows a damped oscillation for about half of the total number. The oscillations do not vanish after a sampling over different initial configurations. The system is in nonequilibrium due to the pressure equilibration, and here the flow is actually compressible. The equilibration time (in time steps) decreases with decreased size of aperture in the partition. For very small apertures (equal or less than$9\frac{\sqrt{3}}{2}$lattice units), the number of molecules in one vessel changes with time in a smooth way until it reaches half of the total number; their curves obey the analytical solution for quasi-static processes. The calculations on$\overline{v_x^2}/\overline{v_y^2}$andΔUalso support the results that the equilibration time decreases with decreased size of aperture in the partition.