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Matem. Mod., 2015, Volume 27, Number 2, Pages 34–62 (Mi mm3570)  

This article is cited in 3 scientific papers (total in 3 papers)

Even- and odd-parity kinetic equations of particle transport. 3: Finite analytic scheme on tetrahedra

A. V. Shilkov

Keldysh Institute of Applied Mathematics RAS, Moscow

Abstract: We derive a finite analytic (not the finite difference) scheme for the even-odd parity transport equations of neutral particles. This discrete scheme utilizes the analytic solution in an adjacent tetrahedral cells to formulate the algebraic representation of partial differential equations. The scheme allows to simulate 3D neutrons and photons transport in heterogeneous absorbing, scattering, multiplying media (problems of nuclear reactors, radiation shielding, radiative heat transfer, radiation gas dynamics) without restrictions on the optical depth of the cell (the product of the extinction coefficient and the cell chord), and no restrictions in the values of jump in extinction coefficient in the transition of particles from one cell to another. Is allowed to change sign the extinction coefficient. The scheme is well combined with different iterative methods for solving deterministic transport problems in which the angular (direction-of-flight) variable is discretized using the discrete-ordinates (Sn) approximation.

Keywords: neutron and photon transport equation, finite analytic method, tetrahedral mesh, numerical simulation, nuclear reactors, radiative heat transfer.

Funding Agency Grant Number
Russian Science Foundation 14-11-00699


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English version:
Mathematical Models and Computer Simulations, 2015, 7:5, 409–429

Received: 23.12.2013

Citation: A. V. Shilkov, “Even- and odd-parity kinetic equations of particle transport. 3: Finite analytic scheme on tetrahedra”, Matem. Mod., 27:2 (2015), 34–62; Math. Models Comput. Simul., 7:5 (2015), 409–429

Citation in format AMSBIB
\Bibitem{Shi15}
\by A.~V.~Shilkov
\paper Even- and odd-parity kinetic equations of particle transport. 3:~Finite analytic scheme on tetrahedra
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 2
\pages 34--62
\mathnet{http://mi.mathnet.ru/mm3570}
\elib{https://elibrary.ru/item.asp?id=23421471}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 5
\pages 409--429
\crossref{https://doi.org/10.1134/S2070048215050117}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84941892405}


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    This publication is cited in the following articles:
    1. A. V. Shilkov, “Reshenie ellipticheskikh uravnenii metodom luchevykh peremennykh”, Preprinty IPM im. M. V. Keldysha, 2017, 119, 36 pp.  mathnet  crossref
    2. A. V. Shilkov, “Uskorenie iteratsii pri reshenii uravneniya perenosa chastits s pomoschyu ekstrapolyatsii istochnika po indeksu iteratsii”, Preprinty IPM im. M. V. Keldysha, 2018, 251, 27 pp.  mathnet  crossref  elib
    3. A. V. Shilkov, “O reshenii lineinykh ellipticheskikh uravnenii vtorogo poryadka”, Matem. modelirovanie, 31:6 (2019), 55–81  mathnet  crossref  elib
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