Statistical simulation of internal energy exchange in shock waves using explicit transition probabilities

A statistical model originally developed for electronic-translational energy transfer in atoms having multiple electronic states (Anderson et al, RGD15, 1986) is applied to the study of internal energy exchange in a polyatomic gas. The model is well-suited for gas kinetic simulations, because it provides an explicit expression for the transition probabilities between internal energy levels. All molecules possessing a given internal energy level are treated as a separate chemical species and all collisions involving exchange of internal energy thus become pseudo-chemical reactions. Post-collision energy levels of the two partners are determined by conserving the total energy of the collision pair and taking into account detailed balance. In the present work, DSMC simulations of relaxation in a stationary gas are performed and compared to those obtained by Anderson et al. Additionally, we apply the model to the simulation of rotational relaxation behind a normal shock wave.