Abstract This paper paves the way to numerically solve the k-eigenvalue neutron transport equation with complex variable arguments, and then employs the developed complex variable transport solver to calculate the k-eigenvalue sensitivities with respect to nuclear cross sections using the complex-step derivative method (CDM). CDM utilizes the Taylor series expansion in the complex plane whereby the imaginary component of the complex solution space can be directly used to represent the sensitivity derivative. CDM offers a robust numerical avenue to calculate accurate sensitivities not susceptible to subtractive cancellation errors. Numerical examples with one-dimensional k-eigenvalue neutron transport models in both one-group and multigroup formulations were employed to demonstrate the feasibility of CDM in reactor problems. The CDM sensitivity results received good agreements to the reference solutions from the conventional forward-based and adjoint-based sensitivity methods. These preliminary results confirmed the viability and accuracy of CDM for k-eigenvalue sensitivity calculation in neutron transport models.

中文翻译：

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复阶导数法在中子输运模型中k特征值灵敏度计算中的应用

摘要 本文为数值求解具有复变量参数的 k 特征值中子输运方程铺平了道路，然后使用开发的复变量输运求解器，使用复阶导数法计算了关于核截面的 k 特征值灵敏度。 (清洁发展机制)。CDM 在复平面中利用泰勒级数展开，从而可以直接使用复解空间的虚部来表示灵敏度导数。CDM 提供了一种强大的数值方法来计算不受减法抵消误差影响的准确灵敏度。在一组和多组公式中具有一维 k 特征值中子输运模型的数值例子被用来证明 CDM 在反应堆问题中的可行性。CDM 灵敏度结果与传统的基于前向和基于伴随的灵敏度方法的参考解决方案得到了很好的一致。这些初步结果证实了 CDM 在中子输运模型中 k 特征值灵敏度计算的可行性和准确性。