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Matematicheskoe modelirovanie, 1996, Volume 8, Number 12, Pages 3–28 (Mi mm1646)  

This article is cited in 11 scientific papers (total in 11 papers)

Mathematical models and computer experiment

A nonlinear method for solving the problems of radiation transfer in medium

D. Yu. Anistratov, E. N. Aristova, V. Ya. Gol'din

Institute for Mathematical Modelling, Russian Academy of Sciences
Abstract: A nonlinear method is described for solving the time-dependent multigroup radiative transfer equation coupled with the energy balance equation. The method is based on the Quasi-Diffusion approach. The idea of this approach is to reduce problem dimension by averaging the equations over angular and energy variables. The functionals weakly depending on the solution of problem are introduced to close equivalently the resulting system of equations. The temperature is determined by solving the linearized energy balance and the efficient grey quasi-diffusion equations. The Frechet derivative of an averaged absorption cross-section with respect to temperature is used to improve the solution of the linearized equations. The one-dimensional geometries are considered. The numerical results are presented to show the efficiency of the proposed method.
Received: 06.07.1995
Bibliographic databases:
Language: Russian
Citation: D. Yu. Anistratov, E. N. Aristova, V. Ya. Gol'din, “A nonlinear method for solving the problems of radiation transfer in medium”, Mat. Model., 8:12 (1996), 3–28
Citation in format AMSBIB
\Bibitem{AniAriGol96}
\by D.~Yu.~Anistratov, E.~N.~Aristova, V.~Ya.~Gol'din
\paper A~nonlinear method for solving the problems of radiation transfer in medium
\jour Mat. Model.
\yr 1996
\vol 8
\issue 12
\pages 3--28
\mathnet{http://mi.mathnet.ru/mm1646}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1472407}
\zmath{https://zbmath.org/?q=an:0984.78503}
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  • https://www.mathnet.ru/eng/mm/v8/i12/p3
  • This publication is cited in the following 11 articles:
    1. E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritma resheniya zadach perenosa izlucheniya v srede”, Preprinty IPM im. M. V. Keldysha, 2024, 064, 27 pp.  mathnet  crossref
    2. N. I. Karavaeva, “Bikompaktnye skhemy dlya resheniya odnogruppovoi sistemy uravnenii kvazidiffuzii sovmestno s uravneniem energii”, Preprinty IPM im. M. V. Keldysha, 2023, 025, 16 pp.  mathnet  crossref
    3. E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy dlya HOLO-algoritma resheniya uravneniya perenosa izlucheniya sovmestno s uravneniem energii”, Kompyuternye issledovaniya i modelirovanie, 15:6 (2023), 1429–1448  mathnet  crossref
    4. S. A. Grabovenskaya, V. V. Zaviyalov, A. A. Shestakov, “Two approaches to effectively reduce the size of radiative heat transfer problems in multidimensional geometry”, Math. Models Comput. Simul., 14:2 (2022), 289–296  mathnet  crossref  crossref
    5. N. Ya. Moiseev, “Modified method of splitting with respect to physical processes for solving radiation gas dynamics equations”, Comput. Math. Math. Phys., 57:2 (2017), 306–317  mathnet  crossref  crossref  isi  elib
    6. Anistratov D.Y., Cornejo L.R., Jones J.P., “Stability Analysis of Nonlinear Two-Grid Method For Multigroup Neutron Diffusion Problems”, J. Comput. Phys., 346 (2017), 278–294  crossref  mathscinet  zmath  isi  scopus
    7. Tamang A., Anistratov D.Y., “A Multilevel Projective Method For Solving the Space-Time Multigroup Neutron Kinetics Equations Coupled With the Heat Transfer Equation”, Nucl. Sci. Eng., 177:1 (2014), 1–18  crossref  isi  elib  scopus
    8. N. Ya. Moiseev, “Explicit-implicit difference scheme for the joint solution of the radiative transfer and energy equations by the splitting method”, Comput. Math. Math. Phys., 53:3 (2013), 320–335  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. E. N. Aristova, “Analog for monotone scheme for calculation of non self-conjugated system of quasi-diffusion equations in rz-geometry”, Math. Models Comput. Simul., 1:6 (2009), 745–756  mathnet  crossref  zmath
    10. E. N. Aristova, A. B. Iskakov, “LATRANT: dvumernaya lagranzhevaya metodika rascheta techenii izluchayuschego gaza v prilozhenii k zadacham UTS”, Matem. modelirovanie, 16:3 (2004), 63–77  mathnet  zmath
    11. V. Ya. Goldin, G. A. Pestryakova, Yu. V. Troschiev, E. N. Aristova, “Samoreguliruemyi neitronno-yadernyi rezhim v reaktore s zhestkim spektrom i karbidnym toplivom”, Matem. modelirovanie, 14:1 (2002), 27–40  mathnet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
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