Numerical analysis
Numerical analysis of the neutron multigroup SP N equations
Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 533-545.

The multigroup neutron SP N equations, which are an approximation of the neutron transport equation, are used to model nuclear reactor cores. In their steady state, these equations can be written as a source problem or an eigenvalue problem. We study the resolution of those two problems with an H 1 -conforming finite element method and a Discontinuous Galerkin method, namely the Symmetric Interior Penalty Galerkin method.

Les équations de la neutronique SP N multigroupe, qui sont une approximation de l’équation de transport des neutrons, sont utilisées pour la modélisation des cœurs de réacteurs nucléaires. Dans le cas stationnaire, ces équations sont soit un problème à source, soit un problème aux valeurs propres. Nous étudions l’approximation de ces deux problèmes avec une méthode d’éléments finis conformes dans H 1 et une méthode d’éléments finis discontinus appelée Symmetric Interior Penalty Galerkin.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.189
Jamelot, Erell 1; Madiot, François 2

1 Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191, Gif-sur-Yvette, France
2 Université Paris-Saclay, CEA, Service d’Études des Réacteurs et de Mathématiques Appliquées, 91191, Gif-sur-Yvette, France
@article{CRMATH_2021__359_5_533_0,
     author = {Jamelot, Erell and Madiot, Fran\c{c}ois},
     title = {Numerical analysis of the neutron multigroup $SP_N$ equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {533--545},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {5},
     year = {2021},
     doi = {10.5802/crmath.189},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.189/}
}
TY  - JOUR
AU  - Jamelot, Erell
AU  - Madiot, François
TI  - Numerical analysis of the neutron multigroup $SP_N$ equations
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 533
EP  - 545
VL  - 359
IS  - 5
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.189/
DO  - 10.5802/crmath.189
LA  - en
ID  - CRMATH_2021__359_5_533_0
ER  - 
%0 Journal Article
%A Jamelot, Erell
%A Madiot, François
%T Numerical analysis of the neutron multigroup $SP_N$ equations
%J Comptes Rendus. Mathématique
%D 2021
%P 533-545
%V 359
%N 5
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.189/
%R 10.5802/crmath.189
%G en
%F CRMATH_2021__359_5_533_0
Jamelot, Erell; Madiot, François. Numerical analysis of the neutron multigroup $SP_N$ equations. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 533-545. doi : 10.5802/crmath.189. http://www.numdam.org/articles/10.5802/crmath.189/

[1] Alonso, Ana; Russo, Anahí D. Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods, J. Comput. Appl. Math., Volume 223 (2009) no. 1, pp. 177-197 | DOI | MR | Zbl

[2] Babuška, Ivo; Osborn, John E. Eigenvalue problems, Handbook of numerical analysis, vol. II (Handbook of Numerical Analysis), Volume 2, North-Holland, 1991, pp. 645-785 | Zbl

[3] Baudron, A.-M.; Lautard, Jean-Jacques Simplified P N transport core calculations in the Apollo3 system International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011)

[4] Brezis, Haim Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, 2010 | Zbl

[5] Ciarlet, Patrick Jr.; Giret, L.; Jamelot, Erell; Kpadonou, F. D. Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients, ESAIM, Math. Model. Numer. Anal., Volume 52 (2018) no. 5, pp. 2003-2035 | DOI | MR | Zbl

[6] Ciarlet, Patrick Jr.; Jamelot, Erell; Kpadonou, F. D. Domain decomposition methods for the diffusion equation with low-regularity solution, Comput. Math. Appl., Volume 74 (2017) no. 10, pp. 2369-2384 | DOI | MR | Zbl

[7] Ciarlet, Philippe G. Linear and nonlinear functional analysis with applications, Society for Industrial and Applied Mathematics, 2013 | Zbl

[8] Dautray, Robert; Lions, Jacques-Louis Analyse mathématique et calcul numérique pour les sciences et les techniques, Masson, 1985 | Zbl

[9] Di Pietro, Daniele Antonio; Ern, Alexandre Mathematical aspects of discontinuous Galerkin methods, Mathématiques & Applications, 69, Springer, 2011 | Zbl

[10] Duderstadt, James J.; Hamilton, Louis J. Nuclear reactor analysis, John Wiley & Sons, Inc., 1976

[11] Ern, Alexandre; Guermond, Jean-Luc Theory and practice of finite elements, Applied Mathematical Sciences, 159, Springer, 2013 | Zbl

[12] Gelbard, E. M. Application of spherical harmonics method to reactor problems, 1960 (Bettis Atomic Power Laboratory, West Mifflin, PA, Technical Report No. WAPD-BT-20)

[13] Giret, L. Non-conforming domain decomposition for the multigroup neutron SPN equation, Ph. D. Thesis, Paris Saclay (2018)

[14] Lautard, Jean-Jacques; Loubière, S.; Fedon-Magnaud, C. CRONOS: a modular computational system for neutronic core calculations, 1992

[15] Lautard, Jean-Jacques; Moller, J.-Y. Minaret, a deterministic neutron transport solver for nuclear core calculations International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011)

[16] Marchuk, Guriĭ I.; Lebedev, Vyacheslav I. Numerical methods in the theory of neutron transport, Harwood Academic Pub., 1986

[17] Nicaise, Serge; Sändig, Anna-Margarete General interface problems. I, II, Math. Methods Appl. Sci., Volume 17 (1994) no. 6, p. 395-429, 431-450 | DOI | MR | Zbl

[18] Osborn, John E. Spectral approximation for compact operators, Math. Comp., Volume 29 (1975) no. 131, pp. 712-725 | DOI | MR | Zbl

[19] Schneider, D. et al. APOLLO3 ® : CEA/DEN deterministic multi-purpose code for reactor physics analysis (PHYSOR-2016, May 1-5 2016, Sun Valley, Idaho, USA)

[20] Takeda, T.; Ikeda, H. 3-D neutron transport benchmarks, Journal of Nuclear Science and Technology, Volume 28 (1991) no. 7, pp. 656-669 | DOI

Cited by Sources: