RATES OF THERMAL RELAXATION IN DIRECT SIMULATION MONTE-CARLO METHODS

For internal energy relaxation in rarefied gas mixtures, exact relationships are derived between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans' equation. These expressions apply to the Borgnakke-Larsen model for internal energy exchange mechanics and are not limited to the assumption of constant Z. Although Jeans' equation leads to adiabatic relaxation curves, which coalesce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke-Larsen selection probabilities depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, simulation results show that the common assumption P = 1/Z is invalid, in general, and leads to considerably slower relaxation than stipulated by Z in Jeans' equation. Moreover, inconsistent definitions of collision rates appearing in the literature can lead to considerable errors in DSMC models. Finally, for general gas mixtures, Borgnakke-Larsen DSMC kinetics match Jeans' behavior exactly only when using a selection methodology, which prohibits multiple relaxation events during a single collision.