Home New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium
Article
Licensed
Unlicensed Requires Authentication

New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium

  • Guennady A. Mikhailov and Ilia N. Medvedev EMAIL logo
Published/Copyright: October 4, 2021

Abstract

Correlative randomized algorithms are constructed by simple randomization of the algorithm of maximum cross-section (equalization, delta tracking) with the use of a one-dimensional distribution and the correlation function or only correlation length of a random medium. The value of the used correlation length can be adjusted using simple test studies. The calculations carried out confirmed the practical effectiveness of the new algorithms.

MSC 2010: 85A25
  1. Funding: The work was completed within the framework of the state task for ICM&MG of Siberian Branch of RAS No. 0251–2021–0002.

References

[1] A. Y. Ambos and G. A. Mikhailov, Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium. Russ. J. Numer. Anal. Math. Modelling 33 (2018), No. 3, 161–171.10.1515/rnam-2018-0014Search in Google Scholar

[2] W. A. Coleman, Mathematical verification of a certain Monte Carlo sampling technique and applications of the techniques to radiation transport problems. J. Nucl. Sci. Engrg. 32 (1968), No. 1, 76–81.10.13182/NSE68-1Search in Google Scholar

[3] B. Davison, Neutron Transport Theory. Oxford University Press, Oxford, UK, 1957.Search in Google Scholar

[4] G. N. Glazov and G. A. Titov, Statistical characteristics of the attenuation coefficient in a broken cloud cover, I. Model with balls of equal radius. In: Issues of Laser Sensing of the Atmosphere, Novosibirsk, 1976, pp. 126–139 (in Russian).Search in Google Scholar

[5] I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Related Variables.Nauka, Moscow, 1965 (in Russian).Search in Google Scholar

[6] C. Larmier, A. Zoia, F. Malvagi, E. Dumonteil, and A. Mazzolo, Monte Carlo particle transport in random media: The effects of mixing statistics. J. Quantitative Spectroscopy and Radiative Transfer 196 (2017), 270–286.10.1016/j.jqsrt.2017.04.006Search in Google Scholar

[7] G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics. Springer, Berlin–Heidelberg, 1980.10.1007/978-3-540-35237-2Search in Google Scholar

[8] I. N. Medvedev and G. A. Mikhailov, Randomized exponential transformation algorithm for solving the stochastic problems of gamma-ray transport theory. Russ. J. Numer. Anal. Math. Modelling 35 (2020), No. 3, 153–162.10.1515/rnam-2020-0012Search in Google Scholar

[9] G. A. Mikhailov, Randomized Monte Carlo algorithms for problems with random parameters (‘double randomization’ method). Numer. Anal. Appl. 12 (2019), 155–165.10.1134/S1995423919020058Search in Google Scholar

[10] G. A. Mikhailov and T. A. Averina, The maximal section algorithm in the Monte Carlo method. Doklady Math. 80 (2009), No. 2, 671–673.10.1134/S1064562409050111Search in Google Scholar

[11] J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems. Addison-Wesley Pub. Co., 1969.Search in Google Scholar

[12] E. Woodcock, T.Murphy, P.Hemmings, and S. Longworth, Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry. In: Proc. Conf. Applications of Computing Methods to Reactor Problems. Vol. 557, 1965, p. 2.Search in Google Scholar

Received: 2021-04-07
Accepted: 2021-05-25
Published Online: 2021-10-04
Published in Print: 2021-08-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 9.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/rnam-2021-0018/pdf
Scroll to top button