Direct Simulation Scheme Derived from the Boltzmann Equation. III. Rough Sphere Gases

TLDR: In this article, the authors derived a stochastic law that describes the collision process in a simulation cell for a gas of rough sphere molecules from the Boltzmann equation for a spatially uniform gas.

Abstract: The stochastic law that describes the collision process in a simulation cell was derived for a gas of rough sphere molecules from the Boltzmann equation for a spatially uniform gas. This law that determines the velocity and angular velocity of each simulated molecule after a small time increment is divided into four steps. The first step gives the collision probability of a molecule. The second step gives a probability distribution that prescribes the collision partner of the molecule. The third step gives a probability density that prescribes the direction of the line-of-centers of the collision pair. The last step gives the post-collision values of the velocity and angular velocity of the molecule.