Statistical fluctuations in Monte Carlo calculations

The time counter and modified Nanbu simulation techniques are analyzed, with emphasis placed on the convergence of the calculations to a steady macroscopic state. Such variables as translational and rotational temperature, and flow velocity, sampled at several points in the flowfield, are considered. Both macroscopic averages and molecular distribution functions are analyzed. The calculation of inelastic collisions, in which transfer of energy between translational and internal energy modes is performed, is achieved through the use of the Larsen-Borgnakke phenomenological model. It is noted that, with reference to translational temperature, the time counter method shows less statistical scatter than that found with the modified Nanbu simulation technique.