Neutron transport equation numerical algorithm: A discrete ordinate method based multi-group neutron transport code for criticality and shielding analysis

This paper presents a deterministic neutron transport model developed for analyzing nuclear reactor criticality and shielding problems in the three-dimensional Cartesian geometry. The model utilizes the discrete ordinate method (DOM or S N ) for angular discretization and the multi-group approximation for energy variable discretization. The spatial discretization methods implemented in the model include a linear diamond difference (LDD) scheme with step option for negative flux fix-up (LDD-step) and a positivity preserving adaptive weighted diamond difference (AWDD) method. For criticality problems, a nested three-level iteration strategy is applied, which combines power iteration, multi-group iteration, and within-group source iteration, whereas a two-level iteration strategy is used for fixed-source problems. A computer code named Neutron Transport Equation Numerical Algorithm (NETRENA) has been developed to implement this numerical model. The code has been used to solve various benchmark problems related to criticality and fixed-source scenarios. The results indicate that the AWDD scheme demonstrates smoother convergence for all tested problems, while the LDD-step scheme exhibit oscillatory behavior under certain conditions related to space-angle grid resolution. The predictions for neutron flux and the effective multiplication factor ( k eff ) from NETRENA using the AWDD scheme show very good agreement with reference results, proving the robustness of the code.