A hybrid spectral nodal method for multigroup X,Y-geometry discrete ordinates eigenvalue problems

A hybrid spectral nodal method for multigroup X,Y-geometry discrete ordinates eigenvalue problems

A hybrid spectral nodal method is developed for the solution of multigroup discrete ordinates (SN) eigenvalue problems with isotropic scattering in X,Y geometry. In this method, the spectral diamond - spectral Green's function (SD-SGF) hybrid scheme, originally developed for numerically solving...

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Bibliographic Details
Published in:Progress in nuclear energy (New series) Vol. 95; pp. 33 - 39
Main Authors: Silva, Davi José M., Alves Filho, Hermes, Barros, Ricardo C.
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01-03-2017
Elsevier BV
Subjects:
Approximation
Decoupling
Diamonds
Discrete ordinates
Eigenvalue problems
Eigenvalues
Energy multigroup
Fission
Geometry
Green's functions
Hybrid spectral nodal method
Iterative methods
Leakage
Mathematical analysis
Nuclear engineering
Nuclear reactor global calculations
Rectangular geometry
Scattering
Spectra
Discrete ordinates
Rectangular geometry
Nuclear reactor global calculations
Energy multigroup
Eigenvalue problems
Hybrid spectral nodal method
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Summary:A hybrid spectral nodal method is developed for the solution of multigroup discrete ordinates (SN) eigenvalue problems with isotropic scattering in X,Y geometry. In this method, the spectral diamond - spectral Green's function (SD-SGF) hybrid scheme, originally developed for numerically solving multigroup SN eigenvalue problem in slab geometry with no spatial truncation error, is generalized to solve the energy multigroup transverse-integrated SN nodal equations with constant approximation for the group transverse leakage terms. The resulting SD-SGF-constant nodal (SD-SGF-CN) method is more accurate than conventional nodal methods for criticality calculations because it treats both the scattering and fission source terms exactly; the only approximation involves the transverse leakage terms. This is in contrast to the classic multigroup SN nodal methods, wherein the group transverse leakage terms, the scattering source and the fission source are all approximated, hence decoupling angular directions and energy groups in the transverse integrated SN nodal equations. We solve the SD-SGF-CN equations using the partial one-node block inversion (NBI) iterative scheme (inner iterations) for each estimate of the dominant eigenvalue in the conventional power method (outer iterations). We show numerical results to illustrate the accuracy of the present multigroup SD-SGF-CN method for coarse-mesh calculations.
ISSN:0149-1970
1878-4224
DOI:10.1016/j.pnucene.2016.11.003