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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 2, Pages 352–361
(Mi zvmmf4834)
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This article is cited in 12 scientific papers (total in 12 papers)
Estimation of the statistical error of the direct statistical modeling method
M. Yu. Plotnikova, E. V. Shkarupab a Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 1, Novosibirsk, 630090 Russia
b Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 6, Novosibirsk, 630090 Russia
Abstract:
The statistical error of the direct simulation Monte Carlo method for numerical solution of the rarefied gas dynamics problems is investigated. Based on the central limit theorem for Markov processes, asymptotic confidence intervals for the errors connected with the number of time steps are obtained for estimates of the three main macroparameters of the flow (density, velocity, and temperature). For the quantities involved in the expressions for the confidence intervals, practical recommendations are given concerning their numerical evaluation simultaneously with the calculation of the flow macroparameters. The proposed approaches to constructing the confidence intervals are illustrated using the classical problem of heat transfer between two infinite parallel plates as an example.
Key words:
rarefied gas dynamics, direct simulation Monte Carlo method, statistical error, confidence interval.
Received: 02.06.2009 Revised: 22.07.2009
Citation:
M. Yu. Plotnikov, E. V. Shkarupa, “Estimation of the statistical error of the direct statistical modeling method”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 352–361; Comput. Math. Math. Phys., 50:2 (2010), 335–344
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https://www.mathnet.ru/eng/zvmmf4834 https://www.mathnet.ru/eng/zvmmf/v50/i2/p352
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Abstract page: | 403 | Full-text PDF : | 144 | References: | 44 | First page: | 6 |
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