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

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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)

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.

Suggested Citation

  • Yongfa Zhang & Song Li & Lei Liu & Xinwen Zhao & Qi Cai & Qian Zhang, 2025. "Padé Approximation for Solving Coupled Subgroup Neutron Transport Equations in Resonant Interference Media," Mathematics, MDPI, vol. 13(18), pages 1-34, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:3003-:d:1751703
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