RATES OF THERMAL RELAXATION IN DIRECT SIMULATION MONTE-CARLO METHODS

For internal energy relaxation in rarefied gas mixtures, exact relatio nships are derived between the selection probability P employed in dir ect simulation Monte Carlo (DSMC) methods and the macroscopic relaxati on rates dictated by collision number Z in Jeans' equation. These expr essions apply to the Borgnakke-Larsen model for internal energy exchan ge mechanics and are not limited to the assumption of constant Z. Alth ough Jeans' equation leads to adiabatic relaxation curves, which coale sce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke-Larsen selection probabili ties depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, s imulation results show that the common assumption P = 1/Z is invalid, in general, and leads to considerably slower relaxation than stipulate d by Z in Jeans' equation. Moreover, inconsistent definitions of colli sion rates appearing in the literature can lead to considerable errors in DSMC models. Finally, for general gas mixtures, Borgnakke-Larsen D SMC kinetics match Jeans' behavior exactly only when using a selection methodology, which prohibits multiple relaxation events during a sing le collision.