Statistical Error Analysis of the DSMC Method Considering Time Correlations Between Samples

The DSMC method has evolved into a most powerful numerical tool for rarefied gas flow in the past half century. The problems related to accuracy have got much attention in DSMC professions. There are 2 types of errors in the DSMC method. One is termed “statistical error”, and the other is “numerical error”. In the DSMC method, the macroscopic properties are obtained with the sample average of the microscopic information. The simulation results are therefore inherently statistical and statistical errors due to finite sampling need to be fully quantified. Statistical error plays an important role in the DSMC method. However, it has not been well understood as yet. Most of the investigations are based upon the assumption that the successive sample results are independent. It is still not clear how many sampling steps are required to get accurate results. Obviously the time correlations make the theoretical analysis of the statistical error more difficult, which has seldom been taken into accounted in the previous researches. With the autocorrelation function and the modified central limit theorem in the statistics, the time correlations between samples can be quantified. The statistical error of the DSMC method was studied based on the benchmark problem of the Couette flow, in view of the time correlations between samples. Quantitative results show that the time correlations affect the statistical error greatly. The time correlations tend to increase the variance of sampled values of random variables, and it takes almost 100 sample steps for the autocorrelation function to decay to 0.