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Numerical Analysis and Applications

2016 year, number 3

Evaluation of statistical error when calculating velocity and temperature components by the direct simulation Monte Carlo method

Mikhail Yu. Plotnikov1, Elena Valer'evna Shkarupa2
1S.S. Kutateladze Institute of Thermophysics, Siberian Division of the Russian Academy of Sciences, pr. Lavrent'eva, 1, Novosibirsk, 630090, Russia
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentieva, 6, Novosibirsk, 630090, Russia
Keywords: прямое статистическое моделирование, статистическая погрешность, равновесная статистическая физика, direct simulation Monte Carlo method, statistical error, equilibrium statistical physics


The direct simulation Monte Carlo method is now widely used to solve the problems of rarefied gas dynamics. While solving stationary problems a special feature of the method is using dependent sample values of random variables to calculate macroparameters of a gas flow. In this paper, the possibility of using the results of statistical physics to estimate the statistical error of the DSMC method is theoretically analyzed. A simple approach to approximate evaluating the statistical error while calculating components of the velocity and temperature is proposed. The approach is tested on a number of problems.