A deterministic method for transient, three-dimensional neutron transport

A deterministic method for solving the time-dependent, three-dimensional Boltzmann transport equation with explicit representation of delayed neutrons has been developed and evaluated. The methodology used in this study for the time variable is the improved quasi-static (IQS) method. The position, energy, and angle variables of the neutron flux are computed using the three-dimensional (3-D) discrete ordinates code TORT. The resulting time-dependent, 3-D code is called TDTORT. The flux shape calculated by TORT is used to compute the point kinetics parameters (e.g., reactivity, generation time, etc.). The amplitude function is calculated by solving the point kinetics equations using LSODE (Livermore Solver of Ordinary differential Equations). Several transient 1-D, 2-D, and 3-D benchmark problems are used to verify TDTORT. The results show that methodology and code developed in this work have sufficient accuracy and speed to serve as a benchmarking tool for other less accurate models and codes. More importantly, a new computational tool based on transport theory now exists for analyzing the dynamic behavior of complex neutronic systems.