The Solution Method for Ultra-Fine Group Slowing-Down Equations Applicable to Stochastic Media

This study presents an innovative solution method for ultra-fine group slowing-down equations tailored to stochastic media with double heterogeneity (DH), focusing on advanced nuclear fuels such as fully ceramic microencapsulated (FCM) fuel and Mixed Oxide (MOX) fuel. Addressing the limitations of conventional resonance calculation methods in handling DH effects, the proposed UFGSP method (the ultra-fine group slowing-down method with the Sanchez–Pomraning method) integrates the Sanchez–Pomraning technique with the ultra-fine group transport theory to resolve spatially dependent resonance cross-sections in both matrix and particle phases. The method employs high-fidelity geometric modeling, iterative cross-section homogenization, and flux reconstruction to capture neutron self-shielding effects in stochastically distributed media. Validation across seven FCM fuel cases, four poison particle configurations (BISO/QUADRISO, Bi/Tri-structural Isotropic), and four plutonium spot problems demonstrated exceptional accuracy, with maximum deviations in effective multiplication factor keff and resonance cross-sections remaining within ±138 pcm and ±2.4%, respectively. Key innovations include the ability to resolve radial flux distributions within TRISO particles and address resonance interference in MOX fuel matrices. The results confirm that the UFGSP method significantly enhances computational precision for DH problems, offering a robust tool for next-generation reactor design and safety analysis.