Matematicheskoe modelirovanie
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Matem. Mod.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskoe modelirovanie, 2021, Volume 33, Number 9, Pages 35–46
DOI: https://doi.org/10.20948/mm-2021-09-03
(Mi mm4318)
 

Two approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry

S. A. Grabovenskaya, V. V. Zaviyalov, A. A. Shestakov

FSUE «RFNC-VNIITF named after Academ. E.I. Zababakhin»
References:
Abstract: Mathematical modelling of kinetic nonstationary transfer of radiation energy is a laborintensive and consuming task. This is due to nonlinearity and high dimensionality of the system to solve. Generaly the kinetic transfer equation is solved in 7-dimensional phase space, which requires vast computational resources. Historically, some attempts were made to simplify the initial system to solve. But simplifying assumptions can a priori degrade the solution quality. Quasi-diffuse approximation for neutron transfer proposed in 1964 by V.Ya. Gol'din was a meaningful step forward in this direction and later it became one of the effective methods to solve uncharged particle transfer problems. The quasi-diffusion method makes allowance for kinetic effects via coefficients calculated in periodic solving of the kinetic equation. There exist other approaches to simplify the initial system. In 2010 M.Yu. Kozmanov and N.G. Karlyhanov proposed a model for 1D geometry which was ideologically close to the quasi-diffusion algorithm. The coefficients obtained in solving the kinetic equation are entered into the model. The approach is being actively developed at RFNC-VNIITF on practical as well as on theoretical level and the user experience suggests its wide application. The paper briefly describes two models and set out the calculation results for two test problems in 2D axially symmetric geometry.
Keywords: radiative heat transfer, dimensionality reduction, numerical method.
Received: 20.01.2020
Revised: 27.10.2020
Accepted: 01.02.2021
English version:
Mathematical Models and Computer Simulations, 2022, Volume 14, Issue 2, Pages 289–296
DOI: https://doi.org/10.1134/S2070048222020077
Document Type: Article
Language: Russian
Citation: S. A. Grabovenskaya, V. V. Zaviyalov, A. A. Shestakov, “Two approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry”, Matem. Mod., 33:9 (2021), 35–46; Math. Models Comput. Simul., 14:2 (2022), 289–296
Citation in format AMSBIB
\Bibitem{GraZavShe21}
\by S.~A.~Grabovenskaya, V.~V.~Zaviyalov, A.~A.~Shestakov
\paper Two approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry
\jour Matem. Mod.
\yr 2021
\vol 33
\issue 9
\pages 35--46
\mathnet{http://mi.mathnet.ru/mm4318}
\crossref{https://doi.org/10.20948/mm-2021-09-03}
\transl
\jour Math. Models Comput. Simul.
\yr 2022
\vol 14
\issue 2
\pages 289--296
\crossref{https://doi.org/10.1134/S2070048222020077}
Linking options:
  • https://www.mathnet.ru/eng/mm4318
  • https://www.mathnet.ru/eng/mm/v33/i9/p35
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математическое моделирование
    Statistics & downloads:
    Abstract page:254
    Full-text PDF :67
    References:37
    First page:7
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024