Homogenization of the criticality spectral equation in neutron transport
Grégoire Allaire; Guillaume Bal
- Volume: 33, Issue: 4, page 721-746
- ISSN: 0764-583X
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topAllaire, Grégoire, and Bal, Guillaume. "Homogenization of the criticality spectral equation in neutron transport." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.4 (1999): 721-746. <http://eudml.org/doc/193943>.
@article{Allaire1999,
author = {Allaire, Grégoire, Bal, Guillaume},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {eigenvalue problem; periodic heterogeneous domain; nuclear reactor cores computations},
language = {eng},
number = {4},
pages = {721-746},
publisher = {Dunod},
title = {Homogenization of the criticality spectral equation in neutron transport},
url = {http://eudml.org/doc/193943},
volume = {33},
year = {1999},
}
TY - JOUR
AU - Allaire, Grégoire
AU - Bal, Guillaume
TI - Homogenization of the criticality spectral equation in neutron transport
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 4
SP - 721
EP - 746
LA - eng
KW - eigenvalue problem; periodic heterogeneous domain; nuclear reactor cores computations
UR - http://eudml.org/doc/193943
ER -
References
top- [1] R. Alexandre and K. Hamdache, Homogénéisation d'équations cinétiques en milieu perforé. C.R. Acad. Sci. Paris Sér. I 313 (1991) 339-344. Zbl0742.35006MR1126410
- [2] G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518. Zbl0770.35005MR1185639
- [3] G. Allaire and G. Bal, Homogénéisation d'une équation spectrale de transport neutronique. C.R. Acad. Sci. Paris Sér. I 325 (1997) 1043-1048. Zbl0888.45002MR1485627
- [4] G. Allaire and Y. Capdeboscq, Homogenization of a spectral problem for a multigroup neutronic diffusion model. Comput Methods Appl. Mech. Engrg. (to appear). Zbl1126.82346MR1765549
- [5] G. Allaire and F. Malige, Analyse asymptotique spectrale d'un problème de diffusion neutronique. C.R. Acad. Sci. Paris Sér. I 324 (1997) 939-944. Zbl0879.35153MR1450451
- [6] P. Anselone, Collectively compact operator approximation theory and applications to integral equations. Prentice-Hall Englewood Cliffs, N.J. (1971). Zbl0228.47001MR443383
- [7] G. Bal, Couplage d'équations et homogénéisation en transport neutronique. Ph.D. thesis, University of Paris 6, France (1997).
- [8] G. Bal, First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport. SIAM J. Appl. Math, (to appear). Zbl0937.35007MR1718300
- [9] G. Bal and X. Warin, An asymptotic analysis for the homogenization of P.W.R. assemblies - The transport case -. Nuclear Sci. Engng. (submitted).
- [10] P. Benoist, Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités. Note CEA-R 2278 (1964).
- [11] A. Bensoussan, J.L. Lions and G. Papanicolaou, Boundary layers and homogenization of transport processes. Publ. RIMS Kyoto Univ. (1979) 53-157. Zbl0408.60100MR533346
- [12] J. Bussac and P. Reuss, Traité de neutronique. Hermann, Paris (1978).
- [13] F. Chatelin, Spectral approximation of linear operators. Academic Press (1983). Zbl0517.65036MR716134
- [14] R. Dautray and J.L. Lions, Mathematical analysis and numerical methods for Science and Technology, Vol. 6. Springer Verlag, Berlin (1993). Zbl0802.35001MR1295030
- [15] V. Deniz, The theory of neutron leakage in reactor lattices, in Handbook of nuclear reactor calculations. Vol II, Y. Ronen Ed. (1968) 409-508.
- [16] L. Dumas and F. Golse, Homogenization of transport equations. Preprint No. R98003, University of Paris 6, LAN. Zbl0964.35016MR1760042
- [17] E. Frenod and K. Hamdache, Homogenization of transport kinetic equation with oscillating potentials. Proc. Roy. Soc. Edin-burgh Sect. A 126 (1996) 1247-1275. Zbl0881.35011MR1424225
- [18] F. Golse, P.L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76 (1988) 110-125. Zbl0652.47031MR923047
- [19] T. Goudon and F. Poupaud (personal communication).
- [20] E. Larsen, Neutron transport and diffusion in inhomogeneous media I. J. Math. Phys. 16 (1975) 1421-1427. MR391839
- [21] E. Larsen, Neutron transport and diffusion in inhomogeneous media II. Nuclear Sci. Engng. 60 (1976) 357-368.
- [22] E. Larsen and J. Keiler, Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75-81. MR339741
- [23] E. Larsen and M. Williams, Neutron Drift in Heterogeneous Media. Nuclear Sci. Engng. 65 (1978) 290-302.
- [24] F. Malige, Étude mathématique et numérique de l'homogénéisation des assemblages combustibles d'un coeur de réacteur nucléaire. Ph.D. thesis, École Polytechnique, France (1996).
- [25] M. Mokhtar-Kharroubi, Les équations de la neutronique. Ph.D. thesis, University of Paris XIII, France (1987).
- [26] G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608-623. Zbl0688.35007MR990867
- [27] J. Planchard, Méthodes mathématiques en neutronique. Collection de la Direction des Etudes et Recherches d'EDF, Eyrolles (1995).
- [28] F. Santosa and M. Vogelius, First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53 (1993) 1636-1668. Zbl0808.35085MR1247172
- [29] R. Sentis, Study of the corrector of the eigenvalue of a transport operator. SIAM J. Math. Anal. 16 (1985) 151-166. Zbl0609.45002MR772875
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