E. N. Aristova, D. F. Baydin, V. Ya. Gol'din, “Two variants of economical method for solving of the transport equation in $r-z$ geometry on the basis of transition to Vladimirov's variables”, Mat. Model., 18:7 (2006), 43

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Matematicheskoe modelirovanie, 2006, Volume 18, Number 7, Pages 43–52 (Mi mm45)

This article is cited in 11 scientific papers (total in 12 papers)

Two variants of economical method for solving of the transport equation in

r - z

$r-z$ geometry on the basis of transition to Vladimirov's variables

E. N. Aristova^a, D. F. Baydin^b, V. Ya. Gol'din^a

^a Institute for Mathematical Modelling, Russian Academy of Sciences
^b Moscow Institute of Physics and Technology

Full-text PDF (425 kB) Citations (12)

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Abstract: The method for numerical solving of 2D steady transport equation on the basis of transition to the Vladimirov's variables have been suggested. The spatial and angular meshes are rigidly connected in classical variant of Vladimirov's method, that is not convenient in many practical cases. The algorithm for equation solving is suggested with independent construction of these meshes. It allows explicitly resolve the structure of all logarithmical discontinuities of solution, which is immanent for problems with spherical and cylindrical geometry. Two variants of the method has been suggested: pure characteristical one and conservative characteristical method. It has been shown for test problem with exact solution that for rough meshes conservative characteristical method allows to construct solution of high accuracy, especially for quasi-diffusion tensor.

Received: 12.12.2005

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Language: Russian

Citation: E. N. Aristova, D. F. Baydin, V. Ya. Gol'din, “Two variants of economical method for solving of the transport equation in

r - z

$r-z$ geometry on the basis of transition to Vladimirov's variables”, Mat. Model., 18:7 (2006), 43–52

Citation in format AMSBIB

\Bibitem{AriBayGol06}

\by E.~N.~Aristova, D.~F.~Baydin, V.~Ya.~Gol'din

\paper Two variants of economical method for solving of the transport equation in $r-z$ geometry on the basis of transition to Vladimirov's variables

\jour Mat. Model.

\yr 2006

\vol 18

\issue 7

\pages 43--52

\mathnet{http://mi.mathnet.ru/mm45}

\zmath{https://zbmath.org/?q=an:1099.76042}

Linking options:

https://www.mathnet.ru/eng/mm45

https://www.mathnet.ru/eng/mm/v18/i7/p43

This publication is cited in the following 12 articles:

A. I. Lobanov, “Nauchnye i pedagogicheskie shkoly Aleksandra Sergeevicha Kholodova”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 561–579
E. N. Aristova, G. O. Astafurov, “The second order short-characteristics method for the solution of the transport equation on a tetrahedron grid”, Math. Models Comput. Simul., 9:1 (2017), 40–47
E. N. Aristova, D. F. Baydin, B. V. Rogov, “Bicompact scheme for linear inhomogeneous transport equation”, Math. Models Comput. Simul., 5:6 (2013), 586–594
E. N. Aristova, “Bicompact scheme for linear inhomogeneous transport equation in a case of a big optical width”, Math. Models Comput. Simul., 6:3 (2014), 227–238
E. N. Aristova, D. F. Baydin, “Efficiency of quasi-diffusion methods for calculation of crucial parameters of fast reactors”, Math. Models Comput. Simul., 4:6 (2012), 568–573
E. N. Aristova, D. F. Baydin, “Quasidiffusion method realization for fast reactor critical parameters calculation in 3D hexagonal geometry”, Math. Models Comput. Simul., 5:2 (2013), 145–155
E. N. Aristova, B. V. Rogov, “About implementation of boundary conditions in the bicompact schemes for a linear transport equation”, Math. Models Comput. Simul., 5:3 (2013), 199–207
E. N. Aristova, G. A. Pestryakova, S. G. Ponomarev, M. I. Stoinov, “Raschet neitronnykh potokov v otrazhatele pri ispolzovanii novykh uglerodnykh materialov”, Preprinty IPM im. M. V. Keldysha, 2012, 079, 12 pp.
E. N. Aristova, D. F. Baidin, “Ekonomichnyi metod resheniya uravneniya perenosa v 2D tsilindricheskoi i 3D geksagonalnoi geometriyakh dlya metoda kvazidiffuzii”, Kompyuternye issledovaniya i modelirovanie, 3:3 (2011), 279–286
E. N. Aristova, “Analog for monotone scheme for calculation of non self-conjugated system of quasi-diffusion equations in $r-z$ -geometry”, Math. Models Comput. Simul., 1:6 (2009), 745–756
E. N. Aristova, V. Ya. Gol'din, “Low-cost calculation of multigroup neutron transport equations for time-to-time recalculation of averaged over spectrum cross-sections”, Math. Models Comput. Simul., 1:5 (2009), 561–572
E. N. Aristova, V. Ya. Goldin, “Raschet uravneniya perenosa neitronov sovmestno s ravneniyami kvazidiffuzii v $r-z$ geometrii”, Matem. modelirovanie, 18:11 (2006), 61–66

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

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References:	93
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