The multigroup neutron 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 -conforming finite element method and a Discontinuous Galerkin method, namely the Symmetric Interior Penalty Galerkin method.
Les équations de la neutronique 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 et une méthode d’éléments finis discontinus appelée Symmetric Interior Penalty Galerkin.
Revised:
Accepted:
Published online:
Erell Jamelot 1; François Madiot 2
@article{CRMATH_2021__359_5_533_0, author = {Erell Jamelot and Fran\c{c}ois Madiot}, 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}, }
Erell Jamelot; François Madiot. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.189/
[1] 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] Eigenvalue problems, Handbook of numerical analysis, vol. II (Handbook of Numerical Analysis), Volume 2, North-Holland, 1991, pp. 645-785 | Zbl
[3] Simplified transport core calculations in the Apollo3 system International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011)
[4] Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, 2010 | Zbl
[5] 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] 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] Linear and nonlinear functional analysis with applications, Society for Industrial and Applied Mathematics, 2013 | Zbl
[8] Analyse mathématique et calcul numérique pour les sciences et les techniques, Masson, 1985 | Zbl
[9] Mathematical aspects of discontinuous Galerkin methods, Mathématiques & Applications, 69, Springer, 2011 | Zbl
[10] Nuclear reactor analysis, John Wiley & Sons, Inc., 1976
[11] Theory and practice of finite elements, Applied Mathematical Sciences, 159, Springer, 2013 | Zbl
[12] Application of spherical harmonics method to reactor problems, 1960 (Bettis Atomic Power Laboratory, West Mifflin, PA, Technical Report No. WAPD-BT-20)
[13] Non-conforming domain decomposition for the multigroup neutron SPN equation, Ph. D. Thesis, Paris Saclay (2018)
[14] CRONOS: a modular computational system for neutronic core calculations, 1992
[15] 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] Numerical methods in the theory of neutron transport, Harwood Academic Pub., 1986
[17] General interface problems. I, II, Math. Methods Appl. Sci., Volume 17 (1994) no. 6, p. 395-429, 431-450 | DOI | MR | Zbl
[18] Spectral approximation for compact operators, Math. Comp., Volume 29 (1975) no. 131, pp. 712-725 | DOI | MR | Zbl
[19] et al. APOLLO3 : CEA/DEN deterministic multi-purpose code for reactor physics analysis (PHYSOR-2016, May 1-5 2016, Sun Valley, Idaho, USA)
[20] 3-D neutron transport benchmarks, Journal of Nuclear Science and Technology, Volume 28 (1991) no. 7, pp. 656-669 | DOI
Cited by Sources:
Comments - Policy