The spectral Green’s function linear-nodal method for one-speed X, Y-geometry discrete ordinates deep penetration problems

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 linear-nodal equations with linear polynomial approximation for the transverse leakage terms. The resulting SGF-linear-nodal (SGF-LN) equations are solved with the full-node inversion (FNI) iterative scheme, which uses 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.