Vibrational nonequilibrium modeling using direct simulation. I - Continuous internal energy

Abstract

A new class of vibrational nonequilibrium models is introduced for repulsive-attractive intermodular potentials to reproduce on average the relaxation time of Millikan and White over all its domain of validity. Intended to do Monte Carlo simulations, it is proposed at a microscopic scale, in the form of individual probabilities of vibration translation energy exchange p. In this first part the internal energy is assumed to be continuous. The relation linking the required individual probability to the relaxation time to be reproduced is solved thanks to the systematic and exact resolution method, based on the Laplace transformation, that we had proposed earlier. Models previously introduced by Boyd and Bird are found as borderline cases of the present one. Attainment of detailed balance is checked with homogeneous calculations, using the direct simulation Monte Carlo method and the original Borgnakke-Larsen (BL) scheme. Assumption used to develop/? models is discussed in light of numerical results and justified thanks to a recent mathematical study of the BL scheme.