The random ray method for challenging deep-penetration shielding problems: A rigorous comparison with multigroup Monte Carlo

Deep-penetration radiation shielding problems present a significant computational challenge for the standard Monte Carlo (MC) method due to statistical inefficiency in low-flux regions. As a robust alternative, this study investigates The Random Ray Method (TRRM), which is founded on deterministic transport along randomly and uniformly sampled rays. A rigorous comparison between TRRM and the Multigroup Monte Carlo (MGMC) method was conducted by implementing both within a unified computational framework. Performance was assessed using two challenging shielding benchmarks—the three-dimensional Wagner model with thick shielding and a two-dimensional shielding facility with multi-bend maze—under four physics configurations that combines multigroup (47-group) and one-group energy treatments with isotropic and anisotropic scattering. The results show that while both methods agree in high-flux regions, MGMC performance degrades significantly as normalized flux has attenuated by 6–7 orders of magnitude, whereas TRRM remains statistically robust. Consequently, TRRM is several orders of magnitude more efficient in these deep-penetration regions, with its Figure of Merit (FOM) exceeding MGMC's by factors of over 10 4 . Critically, the study reveals that the computational advantage of TRRM is substantially amplified in the most physically realistic scenarios (multigroup with anisotropic scattering). Although these complexities increase TRRM's per-ray computational cost, the significant variance reduction from its global sampling strategy overwhelmingly compensates for it. These findings establish TRRM as a highly efficient deterministic alternative for high-fidelity shielding analyses.