Title: Spectral nodal method for numerically solving two-energy group X,Y geometry neutron diffusion eigenvalue problems

Authors: Dany S. Dominguez, Carlos R.G. Hernandez, Ricardo C. Barros

Addresses: Laboratorio de Computacao Cientifica, Universidade Estadual de Santa Cruz, Rod. Ilheus/Itabuna km 16, 45650000, Ilheus, BA, Brazil. ' Departamento de Ingenieria Nuclear, Facultad de Ciencia y Tecnologia Nuclear, Instituto Superior de Tecnologias y Ciencias Aplicadas, Ave. Salvador Allende y Luaces, AP 6163, Ciudad de la Habana, Cuba. ' Departamento de Modelagem Computacional, Instituto Politecnico, Universidade do Estado do Rio de Janeiro, Rua Alberto Rangel s/n, Vila Nova, 28630-050, Nova Friburgo, RJ, Brazil.

Abstract: We describe in this paper the recent advances in spectral nodal methods applied to diffusion problems in Cartesian geometry for neutron multiplying systems. In particular, we present a constant spectral nodal method for two-energy group X,Y geometry applied to neutron diffusion eigenvalue problems. We consider an arbitrary rectangular spatial grid defined on a two-dimensional rectangular domain and we use a transverse integration procedure to transform the two-dimensional problem into two |one-dimensional| problems wherein the transverse leakage terms are approximated by constants. As a result, we obtain the transverse-integrated constant nodal diffusion equations that we discretise using the spectral nodal method. The discretised balance diffusion equations together with appropriate auxiliary equations, continuity and boundary conditions form the two-energy group X,Y geometry spectral constant nodal diffusion equations. The auxiliary equations have parameters that are to be determined such that the analytical general solutions of the transverse-integrated constant nodal diffusion equations are preserved. We show numerical results to illustrate the method|s accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains.

Keywords: diffusion eigenvalue problems; spectral nodal methods; neutron multiplying systems; neutron diffusion.

DOI: 10.1504/IJNEST.2010.030307

International Journal of Nuclear Energy Science and Technology, 2010 Vol.5 No.1, pp.66 - 79

Published online: 14 Dec 2009 *

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