A universal method of redistributing relaxation energies in inelastic molecular collisions

Abstract

The Larsen–Borgnakke (L–B) model is most widely used to redistribute relaxation energies in direct simulation Monte Carlo (DSMC) method; the relaxation energies in an inelastic collision are determined beforehand and redistributed by sampling from the equilibrium distributions (not locally equilibrium distributions) of these energies that are appropriate to this collision. The present concern focuses on how to redistribute the selected energies when they have been determined to require relaxation. When certain energies are determined to require relaxation and redistribution in an inelastic collision, the hierarchical method and the serial or sequential method are used to complete the L–B procedure. Although the hierarchical method is theoretically accurate, it needs to complete the integration of the joint energy distribution function, so it is not applicable when the energy distribution function has a complex form or contains more than one discontinuous energy. Hence, researchers turn to the serial or sequential method, but the rationality proof of this method implies an assumption of locally thermal equilibrium, so it is obviously not appropriate in the DSMC method usually applied to hypersonic nonequilibrium flows. Then, a new method of redistributing relaxation energies to complete the L–B procedure is proposed, which does not include any integration process; the original form of the energy distribution function is used directly, so it can be expected to have excellent adaptability, especially for complex cases such as energy redistribution of reaction products. The effectiveness, efficiency, and extensive applicability of the method are proved by multiple examples.