An exponential spectral nodal method for one-speed X,Y-geometry deep penetration discrete ordinates problems

Presented here is an exponential spectral nodal method applied to deep penetration X,Y-geometry heterogeneous neutron transport problems in the discrete ordinates (SN) formulation. This numerical method uses the spectral Greenʹs 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 exponential functions. We show in two numerical experiments that the SGF-exponential nodal method (SGF-ExpN) generates very accurate results when compared to the conventional transport nodal methods for coarse-mesh deep penetration SN problems, specially in highly absorbing media.