A spectral nodal method for the solution of the Sn equations in x,y geometry for highly absorbing deep penetration problems

Presented here is an attempt to improve the accuracy of transport nodal methods applied to deep penetration transport problems in x, y-geometry. The resulting nodal method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated SN exponential nodal equations with no spatial truncation error. Based on the physics of deep penetration problems, we approximate the transverse leakage terms by approximate exponential shape functions. We show in numerical calculation that the SGF-Exponential Nodal (SGF-Exp N) method is much more accurate than other transport nodal methods for coarse-mesh deep penetration problems, specially in highly absorbing media. (author)