Analysis of the Ill-Posedness in Subgroup Parameter Calculation Based on Pade Approximation and Research on Improved Methods
Year: 2025
Type: article
Abstract: This paper addresses the ill-posed problem in calculating subgroup parameters for resonance self-shielding within nuclear reactor physics. The conventional Pade approximation method often yields negative subgroup cross-sections lacking physical meaning due to its treatment of overdetermined nonlinear systems, making the subgroup transport equations unsolvable. To overcome this, an optimized Pade approximation method is proposed: a resonance factor criterion is used to select energy groups requiring calculation; a systematic procedure dynamically traverses background cross-section combinations starting from a minimal subgroup number, incrementally increasing it until solutions meeting accuracy constraints with positive parameters are found; and, given the insufficiency of background points, a high-resolution resonance integral table is constructed, particularly for ranges exhibiting significant cross-section variations. Numerical validation confirms the method eliminates negative parameters, ensures physical validity, and significantly improves accuracy across benchmark cases including typical fuel pins, burnt pellets, and Gd-bearing lattices. This approach effectively resolves the ill-posedness of the traditional method, offering a more robust and precise subgroup resonance treatment for high-fidelity core neutronics.
Source: Mathematics
DOI: 10.3390/math13162628
Authors: Yongfa Zhang, Song Li, Lei Liu, Xinwen Zhao, Qi Cai, Qian Zhang
Institutions: Naval University of Engineering, Zhejiang University
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4413416885