A combined approach to the estimation of statistical error of the direct simulation Monte Carlo method

Abstract

Presently, the direct simulation Monte Carlo (DSMC) method is widely used for solving rarefied gas dynamics problems. As applied to steady-state problems, a feature of this method is the use of dependent sample values of random variables for the calculation of macroparameters of gas flows. A new combined approach to estimating the statistical error of the method is proposed that does not practically require additional computations, and it is applicable for any degree of probabilistic dependence of sample values. Features of the proposed approach are analyzed theoretically and numerically. The approach is tested using the classical Fourier problem and the problem of supersonic flow of rarefied gas through permeable obstacle.