Monte Carlo simulation method for the Enskog equation

Abstract

A Monte Carlo simulation method to numerically solve the Enskog equation for a hard-sphere fluid is proposed. The method is based on and extends Bird's direct simulation Monte Carlo method to solve the Boltzmann equation. The main modifications are (a) the two particles of a collision pair are taken from cells separated a distance equal to the diameter of the spheres; (b) the collision rate is enhanced by a factor that accounts for the spatial correlations. The method is applied to uniform shear flow and proved to be consistent with (i) the exact pressure tensor obtained from the Enskog equation at local equilibrium for large shear rates, (ii) the viscous heating equation, and (iii) the Navier-Stokes shear viscosity obtained from the Enskog equation. \textcopyright{} 1996 The American Physical Society.