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Matematicheskoe modelirovanie, 2011, Volume 23, Number 9, Pages 65–88 (Mi mm3155)  

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

On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows

A. I. Khisamutdinova, N. N. Velkerb

a Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
b Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Full-text PDF (623 kB) Citations (2)
References:
Abstract: Publication describes Monte Carlo methods and algorithms for Boltzmann equation for rarefied gases problems in case of large-scale flow areas. We consider imitation or Continuous Time Monte Carlo methods where frequencies of interactions of particles’ pairs depend on difference of particles’ coordinates. The question about reduction computational costs of algorithms is examined using specificity of the problem. First, algorithms of an approximated method are constructed, analyzed and realized. This method is obtained using splitting (over groups of particles) of operator in master equations system. In the second place, we investigate fictitious collisions technique, where the upper bound for the number of interacting pairs is specified. Plane Poiseuille flow (in the field of external forces) problem, Heat transfer problem and Temperature discontinuity propagation problem are numerically solved using developed algorithms. Asymptotical estimates of the computational costs are confirmed with the data of the computational processes and comparative properties of the last one are fixed. Suggested algorithms of the method with splitting allow parallelization of the certain type.
Keywords: statistical modeling, Continuous Time Monte Carlo methods for Boltzmann equation, fictitious collisions technique, approximated method obtained using of splitting over groups of particles, reduction of computational cost.
Received: 17.02.2011
English version:
Mathematical Models and Computer Simulations, 2012, Volume 4, Issue 2, Pages 187–202
DOI: https://doi.org/10.1134/S2070048212020068
Bibliographic databases:
Document Type: Article
UDC: 519.245+519.642+533.7
Language: Russian
Citation: A. I. Khisamutdinov, N. N. Velker, “On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows”, Matem. Mod., 23:9 (2011), 65–88; Math. Models Comput. Simul., 4:2 (2012), 187–202
Citation in format AMSBIB
\Bibitem{KhiVel11}
\by A.~I.~Khisamutdinov, N.~N.~Velker
\paper On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows
\jour Matem. Mod.
\yr 2011
\vol 23
\issue 9
\pages 65--88
\mathnet{http://mi.mathnet.ru/mm3155}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2896217}
\transl
\jour Math. Models Comput. Simul.
\yr 2012
\vol 4
\issue 2
\pages 187--202
\crossref{https://doi.org/10.1134/S2070048212020068}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903637532}
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  • https://www.mathnet.ru/eng/mm3155
  • https://www.mathnet.ru/eng/mm/v23/i9/p65
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математическое моделирование
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    Abstract page:319
    Full-text PDF :114
    References:55
    First page:7
     
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