A Spectral Nodal Method for One-GroupX, Y-Geometry Discrete Ordinates Problems

Abstract

This paper reports on a nodal method that is developed for the solution of one-group discrete ordinates (S{sub N}) problems with linearly anisotropic scattering in x, y-geometry. In this method, the spectral Green's function (SGF) scheme, originally developed for solving S{sub N} problems in slab geometry with no spatial truncation error, is generalized to solve the one-dimensional transverse-integrated S{sub N} nodal equations with the constant approximation for the transverse leakage terms. The resulting SGF-constant nodal (SGF-CN) method is more accurate than conventional coarse-mesh methods for deep penetration problems because it treats the scattering source terms implicitly and exactly; the only approximation involves the transverse leakage terms. In conventional S{sub N} nodal methods, the transverse leakage terms and scattering source are both approximated. The authors solve the SGF-CN equations using the one-node block inversion iterative scheme, which uses the best available estimates for the node-entering fluxes to evaluate the node-exiting fluxes in the directions that constitute the incoming fluxes for the adjacent nodes as the equations are swept across the system. Finally, the authors give numerical results that illustrate the accuracy of the SGF-CN method for coarse-mesh calculations.