Computational implementation of analytical methodology for the solution of the neutron transport equation in slab geometry using P_N method

Described in this paper is an analytic methodology for the solution of the neutron transport equation in slab geometry using P_N method. The first part of the present methodology consists of obtaining a local general solution for the P_N equations with arbitrary order 𝑵 L ≤ Nand degree 𝑳 ≤ 𝑵 of scattering anisotropy. In the second part, the local general solution for the P_N equations was replaced in the scattering source of a simplified version of the linear Boltzmann transport equation, i. e., stationary, slab-geometry, monoenergetic, azimuthally symmetric, for non-multiplying media and isotropic internal source. This methodology has been implemented in a computer code developed on the MatLab® platform for Windows. As a result, in addition to generating numerical results for the scalar flux through the P_N method, the computer code generates numerical results for the angular flux at any position in the domain and for any direction not perpendicular to the domain. To evaluate the applicability of the P_N method and the analytic methodology, as described in this paper, numerical results for a model problem are presented. (author)