Probability of inelastic collisions for the Larsen-Borgnakke model to the Monte Carlo simulation method

Abstract

Introduction T HE Larsen-Borgnakke (LB) model has become a standard for calculating inelastic collisions in the Monte Carlo direct simulation method. The essential assumption of the LB model is that the postcollision state of a collision pair is subject to a temporal equilibrium. The model is not a collision-dynamical one but a statistical one. The problem in using the model is how to assign the probabilities of inelastic events in collision. Owing to the very nature of the model, the probabilities of inelastic collisions have no direct connection with measured probabilities or relaxation times, which are of course the outcome of collision dynamics of real molecules. In this Note, the probabilities of inelastic collisions for the LB model are determined in such a way that the difference between the Monte Carlo solution for a very small Knudsen number and the Navier-Stokes solution takes a minimum.