An analysis of the convergence of the direct simulation Monte Carlo method

In this article, a rigorous framework for the analysis of the convergence of the direct simulation Monte Carlo (DSMC) method is presented. It is applied to the simulation of two test cases: an axisymmetric jet at a Knudsen number of 0.01 and Mach number of 1 and a two-dimensional cylinder flow at a Knudsen of 0.05 and Mach 10. The rate of convergence of sampled quantities is found to be well predicted by an extended form of the Central Limit Theorem that takes into account the correlation of samples but requires the calculation of correlation spectra. A simplified analytical model that does not require correlation spectra is then constructed to model the effect of sample correlation. It is then used to obtain an a priori estimate of the convergence error.