On the validity of the Boltzmann equation to describe low density granular systems

TL;DR

This paper investigates the accuracy of the Boltzmann equation in modeling low-density granular gases, comparing simulation methods and analyzing velocity correlations over time.

Contribution

It demonstrates that the Boltzmann equation accurately describes low-density granular systems and explores the effects of velocity parallelization and density dependence.

Findings

Boltzmann equation accurately predicts low-density granular gas behavior

Velocity parallelization plays a significant role over time

Density influences the velocity correlation effects

Abstract

The departure of a granular gas in the instable region of parameters from the initial homogeneous cooling state is studied. Results from Molecular Dynamics and from Direct Monte Carlo simulation of the Boltzmann equation are compared. It is shown that the Boltzmann equation accurately predicts the low density limit of the system. The relevant role played by the parallelization of the velocities as time proceeds and the dependence of this effect on the density is analyzed in detail.