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Hybrid Methods in Engineering

ISSN Print: 1099-2391

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v3.i1.80
15 pages

A HYBRID SPECTRAL NODAL METHOD FOR ONE-SPEED DISCRETE ORDINATES EIGENVALUE PROBLEMS IN TWO-DIMENSIONAL CARTESIAN GEOMETRY

Hermes Alves Filho
Instituto Politécnico—IPRJ, Universidade do Estado do Rio de Janeiro, UERJ, Caixa Postal 97282, 28601-970, Nova Friburgo, RJ, Brazil
Fernando Carvalho Da Silva
Programa de Engenharia Nuclear—COPPE, Universidade Federal do Rio de Janeiro—UFRJ, Caixa Postal 68509, 21 945-970, Rio de Janeiro, RJ, Brazil
Ricardo C. Barros
Instituto Politécnico—IPRJ, Universidade do Estado do Rio de Janeiro, UERJ, Caixa Postal 97282, 28601-970, Nova Friburgo, RJ, Brazil
Member of Editorial Board
2000 - Present Scientific Journal: Progress in Nuclear Energy
Scientific Journal Referee
2007 - 2008 Journal: Annals of Nuclear Energy
1996 - Present Journal: Progress in Nuclear Energy
1995 - Present Journal: Nuclear Science and Engineering

ABSTRACT

We describe a hybrid spectral nodal method applied to one-speed SN eigenvalue problems in X, Y-geometry for nuclear reactor global calculations. To solve the transverse-integrated SN nodal equations, we generalize the spectral diamond (SD) method that we developed for numerically solving slab-geometry SN eigenvalue problems with no spatial truncation error. In the present generalization, we approximate the transverse leakage through the edges of each spatial node by constants, so we call our method the SD-constant nodal (SD-CN) method, which we use in the fuel regions of the nuclear reactor core. In the nonmultiplying regions, for example, reflector and baffle, we use the spectral Green's function-constant nodal (SGF-CN) method; hence the hybrid characteristic of our method. To converge the numerical solution for each SN fixed source problem (inner iterations) in each outer iteration (power method), we use the one-node block inversion (NBI) scheme. We show numerical results for two typical model problems to illustrate the method's accuracy in coarse-mesh calculations and to justify the hybrid characteristic of the numerical algorithm.