Reliable tools to simulate transients are an essential prerequisite for designing new nuclear reactors and assessing their safety. Despite advancements in computer technology and existing neutron transport codes, modeling transients accurately remains resource intensive. This leaves room to explore new transport approaches in the hope they might eventually prove more efficient.

This work builds on The Random Ray Method (TRRM), a stochastic variation of the conventional method of characteristics, which has shown great efficiency in terms of run time and precision for steady-state problems. We propose two modified versions of TRRM for time-dependent applications. The first is a time-implicit (TI) method that converges the spatial distribution at each time step before proceeding to the next. The second employs an unconventional approach by converging the entire space-time configuration simultaneously with time-continuous rays (TCR). Both methods were improved with new features for greater precision and dynamic convergence that were not included in previous versions.

Tested on C5G7-TD benchmark cases 1-2 and 3-4, the proposed methods reproduced the reference results accurately, with mean errors of less than 0.4%. While TI achieved shorter run times and used less memory than TCR, it resulted in slightly higher errors. Overall, the time-dependent TRRM methods in this work required significantly longer computational times than the reference solutions obtained with the code MPACT, which couples high- and low-order methods. Adopting a similar approach for time-dependent TRRM is a potential topic for future research.