The Even Moment Method for Solving the P N Form of the Neutron Transport Equation and Challenges in Computing Multi-Group Transport Cross Sections with Anisotropic Scattering

It has been shown previously that it is possible to transform the PN form of the neutron transport equation into a series of second-order elliptic ordinary differential equations. This so-called even moment method (EMM) has been investigated in the context of the simplified PN approximation, but relatively little effort has been invested in solving the resulting system of equations for materials with anisotropic scattering. In this work, a numerical scheme is derived and demonstrated for solving the PN form of the neutron transport equation via the EMM in the presence of anisotropic scattering for one-dimensional Cartesian geometry. Using the results from this method, computing the transport cross section is then investigated. It is shown that even with accurate results for the flux moments computed from the EMM, computing the transport cross section for use in neutron diffusion methods is challenging due to numerical difficulties and the singularities of the transport cross section.