Mean scattering angle method for direct simulation Monte Carlo.

In order to predict the postcollision velocities in the binary collision, one needs the deflection angle given by the solution of the trajectory equation of classical mechanics. In the direct simulation Monte Carlo, it has been conventional to assume that the scattering is isotropic taking the hard sphere scattering law (the variable hard sphere model). Because the simulation carries out the ensemble average, and thus the collisional deflections should be averaged at the end, it is proposed to use the preaveraged deflection angle for each collision. This is a representative single deflection angle simulation. The present work postulates a method to estimate the mean deflection angles for arbitrary force models considering the differential cross section formula and the trajectory equation. For hard spheres, the representative single deflection simulation of normal shock waves recovers the conventional computations within 3%. For Maxwell molecules, the conventional simulation in which the isotropic scattering law is taken can exactly be reproduced by the single deflection when the representative angle is adjusted to the mean deflection angle together with the reference diameter obtained in the present method. It has been observed that the Maxwell-molecule-representative for the single angle simulation reproduces the conventional computations of any isotropic scattering models including hard spheres.