Padé Approximation for Solving Coupled Subgroup Neutron Transport Equations in Resonant Interference Media

Yongfa Zhang, Song Li (), Lei Liu (), Xinwen Zhao, Qi Cai and Qian Zhang
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Yongfa Zhang: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Song Li: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Lei Liu: College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China
Xinwen Zhao: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Qi Cai: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Qian Zhang: Laboratory for Advanced Nuclear Energy Theory and Applications, Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China

Mathematics, 2025, vol. 13, issue 18, 1-34

Abstract: Resonance self-shielding in multi-resonant nuclide media is a dominant physical process in reactor neutronics analysis. This study proposes an improved subgroup method (ISM) based on Padé rational approximation, constructing a high-order rational function mapping between effective and background cross-sections to overcome the precision bottleneck of traditional DSMs and BIMs in nonlinear resonance interference scenarios. The method first generates cross-section relation data via ultra-fine group calculations, then solves subgroup parameters using a positive definite system, with a Spatial Homogenization (SPH) factor introduced for reaction rate conservation. Validation results show that ISM + SPH reduces k-infinity errors from −708 pcm (DSM) to +5 pcm for UO 2 fuel, and from −269 pcm to +45 pcm for MOX fuel with 239 Pu, significantly enhancing neutron transport accuracy in complex fuel systems. This work provides a theoretically rigorous and practically applicable approach for efficient resonance modeling in advanced reactor fuel design.

Keywords: Padé approximation; rational function approximation; Boltzmann neutron transport equation; resonance self-shielding treatment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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