Homogenization of a spectral problem in neutronic multigroup diffusion

Computer Methods in Applied Mechanics and Engineering

Volumn 187, Issue 1-2, 2000, Pages 91-117

  Allaire, Grégoire ^a,b   Capdeboscq, Yves ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b Lab de Concepts Avancés   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER AIDED ENGINEERING; CRITICALITY (NUCLEAR FISSION); DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; NEUTRONS; REACTOR CORES;

HOMOGENIZED EIGENVECTORS; MULTIGROUP NEUTRON DIFFUSION SYSTEM;

COMPUTATIONAL METHODS;

EID: 0033687309     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00112-7     Document Type: Article

References (30)

1. Allaire G. Homogenization and two-scale convergence. SIAM J. Math. Anal. 23(6):1992;1482-1518.
2. Allaire G., Bal G. Homogénéisation d'une équation spectrale du transport neutronique. C. R. Acad. Sci. Paris Série I, t. 325:1997;1043-1048.
3. G. Allaire, G. Bal, Homogenization of the criticality spectral equation in neutron transport, M2AN, to appear.
4. Allaire G., Malige F. Analyse asymptotique spectrale d'un problème de diffusion neutronique. C. R. Acad. Sci. Paris Série I. t.324:1997;939-944.
5. Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces. SIAM Rev. 18(4):1976;620-710.
6. Anselone P. Collectively Compact Operator Approximation Theory and Applications to Integral Equations. 1971;Prentice-Hall, Englewood Cliffs, NJ.
7. G. Bal, Couplage d'équations et homogénéisation en transport neutronique, Thèse de Doctorat de l'Université paris 6, 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., submitted.
9. G. Bal, X. Warin, An asymptotic analysis for the homogenization of p.w.r. assemblies - the transport case, Nucl. Sci. Eng., submitted.
10. P. Benoist, Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités, Note CEA-R 2278, 1964.
11. Bensoussan A., Lions J.-L., Papanicolaou G. Asymptotic Analysis for Periodic Structures. 1978;North-Holland, Amsterdam.
12. J. Bussac, P. Reuss, Traité de neutronique, Hermann, Paris, 1978.
13. Capdeboscq Y. Homogenization of a diffusion equation with drift. C. R. Acad. Sci. Paris Série I. 327(9):1998;807-812.
14. Chatelin F. Spectral Approximation of Linear Operators. Computer Science and Applied Mathematics. 1983;Academic Press, New York.
15. V. Deniz, The theory of neutron leakage in reactor lattices, in: Y. Ronen (Ed.), Handbook of Nuclear Reactor Calculations, vol. II, CRC Press, Boca Raton, 1986, pp. 409-508.
16. Dorning J.-J., Zhang H., Uddin R. Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion - I: Diffusion equation-based theory. Nucl. Sci. Eng. 121:1995;226-244.
17. D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Comprehensive Studies in Mathematics, Springer, Berlin, 1983.
18. G. Habetler, M. Martino, The multigroup diffusion equations of reactor physics, report KAPL 1886, Knolls Atomic Power Laboratory, 1958.
19. U. Hornung (Ed.), Homogenization and Porous Media, Interdisciplinary Applied Mathematics, vol. 6, Springer, Berlin, 1997.
20. S. Kesavan, Homogenization of elliptic eigenvalue problems part 1 and 2, Appl. Math. Optim. 5 (1979) 153-167, 197-216.
21. Krein M., Rutman M. Linear operators leaving invariant a cone in a Banach space. Functional Anal. Measure Theory. 10:1962;199-325.
22. Larsen E., Hughes R. Homogenized diffusion approximations to the neutron transport equation. Nucl. Sci. Eng. 73:1980;274-280.
23. F. Malige, Etude mathématique et numérique de l'homogénéisation des assemblages combustibles d'un cœur de réacteur nucléaire, Thèse de Doctorat de l' école Polytechnique, 1996.
24. F. Malige, J.-L. Vaudescal, An asymptotic analysis for the systematic homogenization of pwr assemblies, the diffusion case, Technical Report HI-72/97/008/0, EDF-DER, 1997.
25. F. Murat, L. Tartar, H-convergence. Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, mimeographed notes (78), in: A. Cherkaev R.V. Kohn (Eds.), Progress in Nonlinear Differential Equations and their Applications, vol. 31, English translation in topics in the mathematical modelling of composite materials, Birkhaüser, Boston, 1997.
26. Nguetseng G. A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20:1989;608-623.
27. Planchard J. The problem of determining the fine power distribution in reactor fuel assemblies. Progr. Nucl. Energy. 26(1):1991;63-84.
28. J. Planchard, Méthodes mathématiques en neutronique, in: Collection de la Direction des Etudes et Recherches d'EDF, Eyrolles, Paris, 1995.
29. Santosa F., Vogelius M. First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53:1993;1636-1668.
30. Stampacchia G. Le problème de dirichlet pour les équations élliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier. 15(1):1965;189-258.