Conservation of Angular Momentum in the Direct Simulation Monte Carlo Method

Abstract

Meiburg presented the view that the direct simulation Monte Carlo (DSMC) method might not be usable for the computation of vortical flows because the angular momentum is not conserved in collision [Phys. Fluids, 29 (1986) 3107]. In this Letter, that view is clarified. It is first shown that the vorticity is irrelevant to the angular momentum conservation, i.e., it is related to the total linear momentum of molecules in a cell. Since the linear momentum conservation is satisfied in the DSMC method, it is positive that the method is usable in computing vortical flows. Next, it is shown that the expectation of the total angular momentum of molecules in a cell is conserved in the DSMC method; the variance of it is proportional to the square of the cell dimension, so that the smaller the cell, the more accurately the angular momentum conservation is satisfied.