Velocity distribution function of a dilute gas under uniform shear flow: Comparison between a Monte Carlo simulation method and the Bhatnagar-Gross-Krook equation.

Abstract

A Monte Carlo simulation method is used to study a dilute gas of hard spheres under uniform shear flow in the hydrodynamic regime over a wide range of shear rates. The results for the components of the pressure tensor and also for the distribution function are presented and compared with those obtained by using the Bhatnagar-Gross-Krook model kinetic equation. The agreement is fairly good for the pressure tensor and also for the velocity distribution function in the small-velocity region, while discrepancies appear for large velocities. The possibility of using a maximum-entropy method to construct an approximate distribution function is discussed. It is shown that the inclusion of the pressure tensor leads to a distribution function significantly different from the one obtained in the simulation.