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 Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 853–863 (Mi zvmmf11080)

Analysis of the quasi-transfer approximation in problems with analytical solution

A. A. Shestakov

Russian Federal Nuclear Center – All-Russian Research Institute of Technical Physics, Snezhinsk, Chelyabinsk oblast, 456770 Russia

Abstract: The quasi-transfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this case, it is very important to know the behavior of the correction coefficients, because, for the correctness of the diffusion equation, it is necessary that the diffusion coefficient be positive. This can be verified most easily in problems having analytical solutions. The aim of this work is to study the quasi-transfer approximation in problems with an analytical solution and the behavior of correction coefficients in optically dense and transparent media.

Key words: radiative heat transfer, approximations of the transfer equation.

DOI: https://doi.org/10.31857/S0044466920050154

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 833–843

Bibliographic databases:

UDC: 517.958:536.2
Revised: 05.10.2019
Accepted:14.01.2020

Citation: A. A. Shestakov, “Analysis of the quasi-transfer approximation in problems with analytical solution”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 853–863; Comput. Math. Math. Phys., 60:5 (2020), 833–843

Citation in format AMSBIB
\Bibitem{She20} \by A.~A.~Shestakov \paper Analysis of the quasi-transfer approximation in problems with analytical solution \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2020 \vol 60 \issue 5 \pages 853--863 \mathnet{http://mi.mathnet.ru/zvmmf11080} \crossref{https://doi.org/10.31857/S0044466920050154} \elib{https://elibrary.ru/item.asp?id=42687704} \transl \jour Comput. Math. Math. Phys. \yr 2020 \vol 60 \issue 5 \pages 833--843 \crossref{https://doi.org/10.1134/S0965542520050152} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000544378300008} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087181437} 

• http://mi.mathnet.ru/eng/zvmmf11080
• http://mi.mathnet.ru/eng/zvmmf/v60/i5/p853

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. A. Grabovenskaya, V. V. Zavyalov, A. A. Shestakov, “O dvukh podkhodakh effektivnogo ponizheniya razmernosti dlya zadach perenosa teplovogo izlucheniya v mnogomernoi geometrii”, Matem. modelirovanie, 33:9 (2021), 35–46