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

Abstract

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.