Abstract

This paper presents a new robust scheme for coupled physics nuclear reactor calculations. We focus specifically on high-fidelity whole-core transport calculations with coarse mesh finite difference (CMFD) coupled to thermal hydraulics. These simulations traditionally employ rthe Picard iteration for the coupled solution, where it has been observed that the use of CMFD (or nonlinear diffusion acceleration) is detrimental to the overall convergence of the coupled problem. Moreover, (1) if the acceleration equations are tightly converged every iteration, the overall multiphysics iteration becomes less stable and (2) properly loosening the convergence criteria of the acceleration equations at each iteration can stabilize the overall scheme. In this paper, we develop a Fourier analysis for a simplified CMFD-accelerated neutron transport problem with feedback from flux-dependent cross sections to provide a theoretical explanation for, and gain insight into, the aforementioned observations. Furthermore, we establish the theoretical relationship between relaxation and partial convergence of the low-order problem. Using this result, a relaxation-free iteration scheme is then proposed, with a formula to determine the nearly optimal partial convergence of the low-order diffusion problem. The new CMFD method is called the nearly optimally partially converged coarse mesh finite difference (NOPC-CMFD) method. It is shown theoretically that the NOPC-CMFD method in problems with feedback has stability properties comparable to CMFD in problems without feedback and requires no relaxation factor, i.e., is relaxation free. The results presented in this paper provide a theoretical foundation for the development of a robust multiphysics iteration scheme for nuclear reactor modeling. The implementation of the method and application to various test cases are presented in the companion paper.

摘要

本文提出了一种新的用于耦合物理核反应堆计算的稳健方案。我们特别关注具有与热工水力耦合的粗网格有限差分 (CMFD) 的高保真全核输运计算。这些模拟传统上使用 rthe Picard 迭代进行耦合解决方案，其中已经观察到使用 CMFD（或非线性扩散加速）对耦合问题的整体收敛有害。此外，(1) 如果加速度方程在每次迭代中都紧密收敛，则整个多物理场迭代会变得不太稳定；(2) 在每次迭代时适当放松加速度方程的收敛标准可以稳定整个方案。在本文中，我们针对简化的 CMFD 加速中子输运问题开发了傅里叶分析，并提供来自通量相关截面的反馈，为上述观察提供理论解释并深入了解。此外，我们建立了低阶问题的松弛和部分收敛之间的理论关系。使用这个结果，然后提出了一个无松弛迭代方案，用一个公式来确定低阶扩散问题的近似最优部分收敛。新的 CMFD 方法称为近似最优部分收敛的粗网格有限差分 (NOPC-CMFD) 方法。理论上表明，NOPC-CMFD 方法在有反馈问题中具有与无反馈问题中 CMFD 相当的稳定性特性，并且不需要松弛因子，即，是免费的放松。本文中提出的结果为开发用于核反应堆建模的稳健多物理场迭代方案提供了理论基础。配套论文中介绍了该方法的实现和对各种测试用例的应用。