Coupled internal energy modes in DSMC

Abstract

The Landau–Teller model for vibrational energy relaxation of gases toward equilibrium is a first-order kinetic model where the rate of relaxation is proportional to the current defect between the energy in that mode and the equilibrium amount of energy in the mode. In Direct Simulation Monte Carlo (DSMC), collisions are first resolved using a total collision cross section; then, if a collision occurs, the internal energy modes of the colliding particles are tested for relaxation. To reproduce the Landau–Teller model in gases with multiple internal modes, the relaxation of multiple internal modes in a single DSMC collision must be prohibited. This work provides analytical comparison of model-form differences between four models: (1) Landau–Teller theory, (2) the vibrational master equation for a mixture of harmonic oscillators, and DSMC when (3) allowing or (4) prohibiting multiple relaxation in a single collision. This is followed by a rigorous examination of the quantitative effect of the algorithmic choice of allowing or prohibiting multiple relaxation in DSMC. The deviation from the Landau–Teller model caused by allowing multiple relaxations in DSMC is minimal compared to the statistical noise in most cases. However, DSMC practitioners are advised to carefully consider the importance of direct coupling between internal modes, as neglecting these can lead to significant errors.