Inelastic collision selection procedures for direct simulation Monte Carlo calculations of gas mixtures

A modification to existing phenomenological inelastic collision selection procedures suitable for modeling the internal energy exchange processes of gas mixtures in direct simulation Monte Carlo calculations is presented. The selection procedure does not depend on the relative order of rotational and vibrational relaxation processes and does not require the solution of a quadratic equation for every collision to determine the inelastic collision probability. The simulated relaxation process resulting from the selection procedure is analytically proven to be equivalent to the procedures of Haas et al. ["Rates of thermal relaxation in direct simulation Monte Carlo methods," Phys. Fluids6, 2191-2201 (1994)] and the modified procedure of Gimelshein et al. ["Vibrational relaxation rates in the direct simulation Monte Carlo method," Phys. Fluids14, 4452-4455 (2002)]. The implementation and computational efficiency of each of the procedures are discussed. The proposed selection procedure is verified to accurately simulate rotational and vibrational processes for gas mixtures through isothermal relaxation simulations compared with analytical solutions using the Jeans equation.