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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.

Abstract

Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.