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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1494–1518 (Mi zvmmf433)  

This article is cited in 2 scientific papers (total in 3 papers)

Monte Carlo methods in applied mathematics and computational aerodynamics

O. M. Belotserkovskiia, Yu. I. Khlopkovb

a Institute of Automated Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 18/2, Moscow, 123056, Russia
b Zhukovsky Central Institute of Aerohydrodynamics, ul. Zhukovskogo 1, Zhukovskii, Moscow oblast, 140186, Russia

Abstract: A survey of the Monte Carlo methods developed in the computational aerodynamics of rarefied gases is given, and application of these methods in unconventional fields is described. A short history of these methods is presented, and their advantages and drawbacks are discussed. A relationship of the direct statistical simulation of aerodynamical processes with the solution of kinetic equations is established; it is shown that the modern stage of the development of computational methods is impossible without the use of the complex approach to the development of algorithms with regard for all the specific features of the problem to be solved (its physical nature, mathematical model, the theory of computational mathematics, and stochastic processes). Possible directions of the development of the statistical simulation methods are discussed.

Key words: Monte Carlo method, computational aerodynamics, survey of computational methods.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1418–1441

Bibliographic databases:

UDC: 519.676
Received: 07.02.2006

Citation: O. M. Belotserkovskii, Yu. I. Khlopkov, “Monte Carlo methods in applied mathematics and computational aerodynamics”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1494–1518; Comput. Math. Math. Phys., 46:8 (2006), 1418–1441

Citation in format AMSBIB
\Bibitem{BelKhl06}
\by O.~M.~Belotserkovskii, Yu.~I.~Khlopkov
\paper Monte Carlo methods in applied mathematics and computational aerodynamics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1494--1518
\mathnet{http://mi.mathnet.ru/zvmmf433}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287365}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1418--1441
\crossref{https://doi.org/10.1134/S0965542506080124}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748331251}


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    3. Veresnikov G.S., Pankova L.A., Pronina V.A., “Uncertain Programming in Preliminary Design of Technical Systems with Uncertain Parameters”, Xii International Symposium Intelligent Systems 2016, (Intels 2016), Procedia Computer Science, 103, eds. Askhat D., Ivan Z., Andrew K., Eugeny N., Elsevier Science BV, 2017, 36–43  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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