Abstract In this work, we attempt to overcome the “curse of dimensionality” inherent to neutron diffusion kinetics problems by employing a novel reduced-order modeling technique known as proper generalized decomposition (PGD). The novelty of this work is that it represents the first attempt at applying PGD reduced-order modeling to time-dependent multigroup neutron diffusion kinetics. The performance of PGD reduced-order models (ROMs) will be quantified by comparing PGD ROMs to reference high-fidelity solutions using Rattlesnake for the TWIGL problem, a standard reactor kinetics benchmark. We show that for problems that exhibit sufficient spatial regularity, our proposed PGD algorithm computes accurate ROMs in less time than the reference high-fidelity calculation. By considering a variation of the TWIGL benchmark that maintains an analogous delayed supercritical behavior but has a smooth spatial solution, we compute PGD ROMs with a maximum relative difference in total power of less than 2.2% using 103 fewer degrees of freedom and a speedup of nearly 13× when compared to reference solutions. However, when introducing the stronger spatial irregularities of the reference benchmark, the accuracy and timing of the proposed PGD algorithm diminishes. We show that by using continuous finite elements, PGD ROMs are subject to undesirable numerical oscillations. In this paper, we motivate the use of PGD in neutron diffusion kinetics, discuss the adopted mathematical framework, and using our results, discuss the challenges and unique aspects of our implementation.

中文翻译：

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使用适当的广义分解对核反应堆动力学进行降阶建模

摘要 在这项工作中，我们试图通过采用一种称为适当广义分解 (PGD) 的新型降阶建模技术来克服中子扩散动力学问题固有的“维数灾难”。这项工作的新颖之处在于它代表了首次尝试将 PGD 降阶建模应用于时间相关的多群中子扩散动力学。PGD​​ 降阶模型 (ROM) 的性能将通过将 PGD ROM 与使用响尾蛇解决 TWIGL 问题（标准反应器动力学基准）的参考高保真解决方案进行比较来量化。我们表明，对于表现出足够空间规律性的问题，我们提出的 PGD 算法可以在比参考高保真计算更短的时间内计算出准确的 ROM。通过考虑保持类似延迟超临界行为但具有平滑空间解的 TWIGL 基准的变体，我们计算 PGD ROM，总功率的最大相对差异小于 2.2%，使用较少的 103 个自由度和近与参考溶液相比为 13 倍。然而，当引入参考基准的更强空间不规则性时，所提出的 PGD 算法的准确性和时间会降低。我们表明，通过使用连续有限元，PGD ROM 会受到不利的数值振荡。在本文中，我们鼓励在中子扩散动力学中使用 PGD，讨论采用的数学框架，并使用我们的结果，讨论我们实施的挑战和独特方面。