A Green-Kubo Approach to Reduce Collision Separation Error in the Direct Simulation Monte Carlo Method

A modification to DSMC collision routines is proposed to eliminate or reduce collision separation error in numerical transport coefficients. This modification follows from earlier DSMC error analysis based on Green-Kubo theory, and is currently limited to the case of a hard sphere monatomic simple gas simulation with approximately isotropic collision separation statistics. Further adjustments to the DSMC collision algorithm are proposed to reduce collision separation error associated with a finite time step interval. It is shown analytically that, for random collision partner selection at the small time step limit with a cell size equal to the mean free path, collision separation error in viscosity is reduced by approximately 37% while thermal conductivity error is completely removed. In a demonstration case involving hypersonic flow over a cylinder, the proposed modification is found to allow for large error reductions in both the total force and heat transfer rate. Although this modification is not intended as a general solution to the problem of DSMC collision separation error, it is hoped that the concept demonstrated here of utilizing Green-Kubo analysis for DSMC error reduction will in the future find more widespread applicability.