Implementation of the time dependent neutron transport algorithm in 2D utilizing modular ray tracing by method of characteristic framework

This paper discusses the implementation of an algorithm for solving 2D time-dependent neutron transport equations in heterogeneous media. A novel modular ray tracing algorithm where neutrons are allowed to travel a longer path before being removed from the structure, is adopted for the transient calculation. The time derivative of angular flux is considered as a major source of challenges in implementing the neutron transport equation, in which two cases for the time derivative of angular flux are included, first, the angular dependency of the time derivative is preserved and second mode, isotropic scalar flux approximation is applied to the time derivative. Sensitivity analysis on time step size has been investigated as an effective parameter on both computational accuracy and cost. Investigating the compatibility of the proposed numerical algorithm as well as considering the substantial role of delayed neutrons in transient processes, three multigroup mathematical models for delayed neutrons are evaluated along with the neutron transport equation. For the implementation of the verification algorithm, the well-known TWIGL benchmark is modeled and the results are compared with MPACT and DeCART codes.