About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 913043, 15 pages
http://dx.doi.org/10.1155/2014/913043
Research Article

Resolution of the Generalized Eigenvalue Problem in the Neutron Diffusion Equation Discretized by the Finite Volume Method

1Institute for Industrial, Radiophysical and Environmental Safety (ISIRYM), Universitat Politècnica de València, 46022 Valencia, Spain
2Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain

Received 31 October 2013; Accepted 22 November 2013; Published 23 January 2014

Academic Editor: Benito Chen-Charpentier

Copyright © 2014 Álvaro Bernal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, New York, NY, USA, 2001.
  2. G. Verdú, D. Ginestar, V. Vidal, and J. L. Muñoz-Cobo, “3D λ-modes of the neutron-diffusion equation,” Annals of Nuclear Energy, vol. 21, no. 7, pp. 405–421, 1994. View at Publisher · View at Google Scholar
  3. R. Miró, D. Ginestar, G. Verdú, and D. Hennig, “A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis,” Annals of Nuclear Energy, vol. 29, no. 10, pp. 1171–1194, 2002. View at Publisher · View at Google Scholar
  4. V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Transactions on Mathematical Software, vol. 31, no. 3, pp. 351–362, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. A. Hoffmann and S. T. Chiang, Computational Fluid Dynamics, vol. 2, Engineering Education System, Wichita, Kan, USA, 4th edition, 2000.
  6. D. J. E. Harvie, “An implicit finite volume method for arbitrary transport equations,” ANZIAM Journal, vol. 52, pp. C1126–C1145, 2012. View at MathSciNet
  7. L. Cueto-Felgueroso, I. Colominas, X. Nogueira, F. Navarrina, and M. Casteleiro, “Finite volume solvers and moving least-squares approximations for the compressible Navier-Stokes equations on unstructured grids,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 45–48, pp. 4712–4736, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Geuzaine and J.-F. Remacle, “Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities,” International Journal for Numerical Methods in Engineering, vol. 79, no. 11, pp. 1309–1331, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. V. Hernández, J. E. Román, and V. Vidal, “SLEPc: scalable library for eigenvalue problem computations,” in High Performance Computing for Computational Science—VECPAR 2002, vol. 2565 of Lecture Notes in Computer Science, pp. 377–391, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar
  10. E. Z. Müller and Z. J. Weiss, “Benchmarking with the multigroup diffusion high-order response matrix method,” Annals of Nuclear Energy, vol. 18, no. 9, pp. 535–544, 1991. View at Scopus