A nodal collocation approximation for the multi-dimensional PL equations – 2D applications

A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the PL equations. In this work, the derivation of the PL equations for multi-dimensional geometries is reviewed and a nodal collocation method is developed to discretize these equations on a rectangular mesh based on the expansion of the neutronic fluxes in terms of orthogonal Legendre polynomials. The performance of the method and the dominant transport Lambda Modes are obtained for a homogeneous 2D problem, a heterogeneous 2D anisotropic scattering problem, a heterogeneous 2D problem and a benchmark problem corresponding to a MOX fuel reactor core.