A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

Zachary K. Hardy, Jim E. Morel, Jan I. C. Vermaak
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Abstract

The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasi-diffusion. While this method has been shown to be comparable to quasi-diffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to thought that the resulting inhomogeneous source makes the problem ill-posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasi-diffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.
连续扩散和非连续传输离散的 k 特征值加速度第二矩方法
第二矩法是一种线性加速技术,它将传输方程与扩散方程耦合在一起,并带有与传输相关的加法闭合。与扩散合成加速法不同的是,由此产生的低阶扩散方程可以独立于传输离散化,而且与准扩散法不同的是,它是对称正定的。虽然这种方法在固定源和时间相关问题的迭代性能上与准扩散法不相上下,但作为特征值问题的加速方案,它在很大程度上未被探索,因为人们认为由此产生的不均匀源会使问题变得难以解决。最近,对第二矩法特征值问题进行了初步可行性研究。研究结果表明,该方法的性能与准扩散法相当,而且比扩散合成加速法更稳健。本研究利用最先进的离散化技术,将初步研究扩展到更现实的反应堆问题。本文的研究结果表明,在非结构网格的复杂反应堆问题上,第二矩法比其他方法的计算效率更高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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