Abstract Numerical instability resulting from coupling isotopic depletion and neutronics is widely reported, but little work has been done to interrogate the phenomenon theoretically. This work extends the pioneering analysis developed by Densmore et al., who examined the stability of a monoenergetic neutron diffusion problem coupled with a simple depletion system through the explicit Euler scheme. Their Fourier stability analysis is applied to the predictor-corrector scheme and its iterated and implicit variants. The results reproduce behaviour described in previous reports of numerical instability and its solution, and develop a future avenue for diagnosing the stability of burn-up problems.

中文翻译：

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耦合中子学和耗尽的预测器-校正器方案的稳定性分析

摘要 同位素耗尽和中子学耦合引起的数值不稳定性被广泛报道，但很少有人从理论上研究这一现象。这项工作扩展了 Densmore 等人开发的开创性分析，他们通过显式欧拉方案检查了单能中子扩散问题与简单耗尽系统的稳定性。他们的傅立叶稳定性分析应用于预测器-校正器方案及其迭代和隐式变体。结果重现了先前关于数值不稳定性及其解决方案的报告中描述的行为，并为诊断燃耗问题的稳定性开辟了未来的途径。