Spectral Nodal Methodology for Multigroup Slab-Geometry Discrete Ordinates Neutron Transport Problems with Linearly Anisotropic Scattering

Abstract

In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that generates numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as a study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (SN) formulation, in slab geometry, multigroup approximation, with linearly anisotropic scattering, considering a heterogeneous domain with fixed-source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional fine-mesh Diamond Difference (DD) method and the coarse-mesh spectral Green's function (SGF) method to illustrate the method's accuracy and stability. The solution algorithms problem is implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work.

Keywords

• Neutron Transport Equation
• Discrete Ordinates Method
• Nodal Methods
• Anisotropic Scattering
• Computational Modeling.