Evaluation of macroscopic properties in the direct simulation Monte Carlo method

General expressions for evaluating macroscopic properties in the direct simulation Monte Carlo (DSMC) method are examined using numerical examples. DSMC simulations show that the evaluations (both statistically dependent and independent) generally follow Gaussian distributions except that the temperature evaluations follow chi-square distributions, whereas their statistical errors mainly depend on the sample size. To reduce the statistical errors for macroscopic properties required during DSMC simulations, a subrelaxation technique is proposed to build up the sample size by including the previous history using a relaxation factor. It is found that the subrelaxation technique helps reduce the statistical errors as if the sample size were increased by a factor of the reciprocal of the relaxation factor. This property makes use of the technique attractive for many DSMC applications.