Spectral-Nodal Deterministic Methodology for Neutron Shielding Calculations using the X, Y - geometry Multigroup Transport Equation in the Discrete Ordinates Formulation

In this work, we present the most recent numerical results in a nodal approach, which resulted in the development of a new numerical spectral nodal method, based on the spectral analysis of the multigroup, isotropic scattering neutron transport equations in the discrete ordinates ($S_N$) formulation for fixed-source calculations in non-multiplying media (shielding problems). The numerical results refer to simulations of typical problems from the reactor physics field, in rectangular two-dimensional Cartesian geometry, $X, Y$ geometry, and are compared with the traditional Diamond Difference ($DD$) fine-mesh method results, used as a reference, and the spectral coarse-mesh method Green's function ($SGF$) results.