SPECTRAL GREEN'S FUNCTION LINEAR-NODAL METHOD FOR MONOENERGETIC X,Y-GEOMETRY EXTERNAL SOURCE DISCRETE ORDINATES PROBLEMS

摘要

A new spectral nodal method is developed for the solution of one-speed discrete ordinates (SN) problems with isotropic scattering in X,Y-geometry. In this method, the spectral Green's function (SGF) scheme, originally developed for solving SN problems in slab geometry with no spatial truncation error, is generalized to solve the one-dimensional transverse-integrated SN nodal equations wherein we consider linear polynomial approximation for the transverse leakage terms. To solve the resulting SGF-linear nodal (SGF-LN) equations we implement the full-node invesion (FNI) iterative scheme, which used the best available estimates for the node-entering quantities to evaluate the node angular quantities in all the exiting directions as the equations are swept across the system. We give numerical results that illustrate the accuracy of the SGF-LN method for coarse-mesh calculations.