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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 352–361 (Mi zvmmf4834)  

This article is cited in 8 scientific papers (total in 8 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.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 335–344

Bibliographic databases:

UDC: 519.676
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Plotnikov M.Yu. Shkarupa E.V., “Selection of sampling numerical parameters for the DSMC method”, Comput. & Fluids, 58 (2012), 102–111  crossref  mathscinet  zmath  isi  scopus
    2. Plotnikov M.Yu. Shkarupa E.V., “Estimation of the statistical error and the choice of parameters in the method of test particles”, Russ. J. Numer. Anal. Math. Model., 27:2 (2012), 155–173  crossref  mathscinet  zmath  isi  elib  scopus
    3. Plotnikov M.Yu., Shkarupa E.V., “Comparison of different approaches to evaluation of statistical error of the DSMC method”, 28th International Symposium on Rarefied Gas Dynamics 2012, v. 1, 2, AIP Conf. Proc., 1501, eds. Mareschal M., Santos A., Amer. Inst. Physics, 2012, 503–510  crossref  adsnasa  isi  scopus
    4. Plotnikov M.Yu., Shkarupa E.V., “Approximate Approach To Evaluation of the Dsmc Statistical Error”, Proceedings of the 29th International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings, 1628, ed. Fan J., Amer Inst Physics, 2014, 305–312  crossref  adsnasa  isi
    5. Plotnikov M.Yu., Shkarupa E.V., “Theoretical and Numerical Analysis of Approaches To Evaluation of Statistical Error of the Dsmc Method”, Comput. Fluids, 105 (2014), 251–261  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. Yu. Plotnikov, E. V. Shkarupa, “A combined approach to the estimation of statistical error of the direct simulation Monte Carlo method”, Comput. Math. Math. Phys., 55:11 (2015), 1913–1925  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Karchani A., Ejtehadi O., Myong R.S., “A Probabilistic Automatic Steady State Detection Method for the Direct Simulation Monte Carlo”, Commun. Comput. Phys., 20:5 (2016), 1183–1209  crossref  mathscinet  zmath  isi  elib  scopus
    8. Myong R.S., Karchani A., Ejtehadi O., “A Review and Perspective on a Convergence Analysis of the Direct Simulation Monte Carlo and Solution Verification”, Phys. Fluids, 31:6 (2019), 066101  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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