Modified Generalized Hard Sphere Collision Model for Direct Simulation Monte Carlo Calculations

Abstract

The generalised hard sphere collision model (GHS) was introduced by Hassan and Hash [Physics of Fluids A, v5(3), 738-744 (1993)] and is a generalization of the Sutherland collision model suggested by Kuscer [Physica, v158, 784-800 (1989)]. Despite its superior modelling of realistic gas viscosities, compared to the Variable Hard Sphere collision model, the GHS model is rarely used because of its great computational expense compared to the VHS model. We show here how a slight modification of the GHS model makes it no more than 15% more computationally expensive than the VHS model, while retaining its superior viscosity modelling. All that is required is that the collision probability be limited for collision speeds approaching zero, rather than increase to infinity as it does for the original GHS model. A particularly simple modification is to use a Maxwell collision cross-section (equal probabilities) for collision energies less than the attractive energy of a realistic molecular model (characteristic temperature T* approximate 90 - 150 K). For temperatures above T*, the GHS viscosity is retained, while for temperatures less than T* the viscosity is slightly different from the GHS viscosity, but arguably more realistic.