Homogenization of the criticality spectral equation in neutron transport

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 4, 1999, Pages 721-746

  Allaire, Grégoire ^a,b   Bal, Guillaume ^a,c  

^a SORBONNE UNIVERSITÉ   (France)

^b Lab de Concepts Avancés   (France)

^c EDF R AND D   (France)

Author keywords

Homogenization; Transport equations

Indexed keywords

EID: 0033469593     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999160     Document Type: Article

References (29)

1. R. Alexandre and K. Hamdache, Homogénéisation d'équations cinétiques en milieu perforé. C.R. Acad. Sci. Paris Sér. I 313 (1991) 339-344.
2. G. Allaire, Homogenization and two scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518.
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.
4. G. Allaire and Y. Capdeboscq, Homogenization of a spectral problem for a multigroup neutronic diffusion model. Comput. Methods Appl. Mech. Engrg. (to appear).
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.
6. P. Anselone, Collectively compact operator approximation theory and applications to integral equations. Prentice-Hall, Englewood Cliffs, N.J. (1971).
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).
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.
12. J. Bussac and P. Reuss, Traité de neutronique. Hermann, Paris (1978).
13. F. Chatelin, Spectral approximation of linear operators. Academic Press (1983).
14. R. Dautray and J.L. Lions, Mathematical analysis and numerical methods for Science and Technology, Vol. 6. Springer Verlag, Berlin (1993).
15. V. Deniz, The theory of neutron leakage in reactor lattices, in Handbook of nuclear reactor calculations, VoI 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.
17. E. Frenod and K. Hamdache, Homogenization of transport kinetic equation with oscillating potentials. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996) 1247-1275.
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.
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.
21. E. Larsen, Neutron transport and diffusion in inhomogeneous media II. Nuclear Sci. Engng. 60 (1976) 357-368.
22. E. Larsen and J. Keller, Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75-81.
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 cœur 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.
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.
29. R. Sentis, Study of the corrector of the eigenvalue of a transport operator. SIAM J. Math. Anal. 16 (1985) 151-166.