Abstract
In this paper, we propose a new deterministic numerical methodology to solve the one-dimensional linearized Boltzmann equation applied to neutron shielding problems (fixed-source), using the transport equation in the discrete ordinates formulation (SN) considering the multigroup theory. This is a hybrid methodology, entitled Modified Spectral Deterministic Method (SDM-M), that derives from the Spectral Deterministic Method (SDM) and Diamond Difference (DD) methods. This modification in the SDM method aims to calculate neutron scalar fluxes with lower computational cost. Two model-problems are solved using the SDM-M, and the results are compared to the coarse-mesh methods SDM, Spectral Green's Function (SGF) and Response Matrix (RM), and the fine-mesh method DD. The numerical results were obtained in the programming language JAVA version 1.8.0_91.
Highlights
Neutron transport modelling have been a crescent research area, due to the many fields that need an accurate knowledge of the neutron flux behavior and it's interactions with the nuclei that constitutes the material zones, e.g., neutron shielding, radiology protection, nuclear medicine and oil prospecting
We propose a deterministic numeric method to solve the linearized Boltzmann equation applied to neutron shielding problems, denominated Modified Spectral Deterministic Method (SDM-M)
The numerical results of SDM-M are compared to the traditional fine-mesh Diamond Difference (DD) and the coarse-mesh methods SDM, Spectral Green's Function (SGF) and Response Matrix (RM)
Summary
Neutron transport modelling have been a crescent research area, due to the many fields that need an accurate knowledge of the neutron flux behavior and it's interactions with the nuclei that constitutes the material zones, e.g., neutron shielding (fixed-source problems), radiology protection, nuclear medicine and oil prospecting. The calculation of the neutron angular flux inside a material zone can be computationally expensive when it comes to solve real world problems. A neutron moving inside a material zone can be described deterministically by the linearized Boltzmann equation, derived for the gas kinetics theory [1,2]. Which is a linear partial integrodifferential equation with 3 spatial variables, 2 angular variables, 1 time variable and 1 energetic variable. This equation represents a balance of production and loss of neutrons, assuming that the interaction of these particles with hosting media does not affect its structure, and there is no interaction between them. The angular variable is treated according to the discrete ordinates formulation (SN), with multigroup method [1]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
