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 Matem. Mod., 2014, Volume 26, Number 3, Pages 75–96 (Mi mm3460)

Even–odd parity transport equations. 1: Algebraic and centered forms of the scattering source

A. V. Shilkov

Keldysh Institute of Applied Mathematics RAS

Abstract: We consider an equivalent formulation of the linear transport equation of neutral particles (neutrons, photons) as a system of two equations for the even and odd parts of the distribution function. The scattering source of the even-odd parity transport equations is transformed into non-linear algebraic form and into centered form. The algebraic form of the source is constructed from the “net result” of two opposite processes — the escape of particles from the beam and the coming of particles in the beam due to scattering processes. To obtain the centered form, compensation of the main contributions of these opposite processes is performed. We propose the iterative method for solving even-odd parity transport equations with algebraic or centered forms of scattering source. The convergence of the iterations in a plane problem has been studied.

Keywords: neutron and photon transport equation, iterative method, numerical simulation, nuclear reactors, radiative heat transfer.

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English version:
Mathematical Models and Computer Simulations, 2014, 6:5, 465–479

Document Type: Article

Citation: A. V. Shilkov, “Even–odd parity transport equations. 1: Algebraic and centered forms of the scattering source”, Matem. Mod., 26:3 (2014), 75–96; Math. Models Comput. Simul., 6:5 (2014), 465–479

Citation in format AMSBIB
\Bibitem{Shi14} \by A.~V.~Shilkov \paper Even–odd parity transport equations. 1:~Algebraic and centered forms of the scattering source \jour Matem. Mod. \yr 2014 \vol 26 \issue 3 \pages 75--96 \mathnet{http://mi.mathnet.ru/mm3460} \elib{http://elibrary.ru/item.asp?id=21826441} \transl \jour Math. Models Comput. Simul. \yr 2014 \vol 6 \issue 5 \pages 465--479 \crossref{https://doi.org/10.1134/S2070048214050123} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925939687} 

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This publication is cited in the following articles:
1. A. V. Shilkov, “Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems”, Math. Models Comput. Simul., 7:1 (2015), 36–50
2. A. V. Shilkov, “Even- and odd-parity kinetic equations of particle transport. 3: Finite analytic scheme on tetrahedra”, Math. Models Comput. Simul., 7:5 (2015), 409–429
3. M. N. Gertsev, A. V. Shilkov, E. N. Aristova, “Raschet perenosa teplovogo izlucheniya v atmosfere Zemli”, Preprinty IPM im. M. V. Keldysha, 2016, 042, 28 pp.
4. 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.
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