Abstract

In a companion paper, we present the theoretical development of a new robust, relaxation-free iteration scheme for multiphysics $k$-eigenvalue problems. These types of problems are essential to the study of computational reactor physics and in particular whole-core, high-fidelity simulation codes. The deterministic whole-core simulation tools invariably rely on the coarse mesh finite difference (CMFD) acceleration for fast convergence. However, the use of CMFD-accelerated transport in multiphysics problems coupled via Picard iteration is not robust and is frequently treated with relaxation. In this paper, we build on our previous theoretical work that uses Fourier analysis to prove how stability and efficient convergence can be achieved in the multiphysics problem by appropriately loosening the convergence criteria of the low-order diffusion acceleration equations. Specifically, we develop a methodology for estimating a key problem-dependent parameter, the feedback intensity, required by the nearly optimally partially converged coarse mesh finite difference (NOPC-CMFD) method. We then describe the implementation of NOPC-CMFD in the Michigan Parallel Characteristics Transport (MPACT) code and perform several numerical calculations. Problems ranging from a single pressurized water reactor (PWR) fuel rod to a full-core PWR cycle depletion are analyzed to assess the performance and robustness of NOPC-CMFD over a wide range of conditions that consider multiple forms of multiphysics feedback. The results verify the theoretical predictions of our companion paper, illustrating that the NOPC-CMFD is superior to current CMFD or nonlinear diffusion acceleration schemes that use relaxation. Overall, the method is able to recover the performance of traditional CMFD in problems without feedback for a wide range of conditions. This was observed to result in a substantial reduction, up to 40%, of the run time in whole-core cycle depletion problems.

摘要

在一篇配套论文中，我们介绍了一种新的稳健、无松弛的多物理场迭代方案的理论发展 $克$- 特征值问题。这些类型的问题对于计算反应堆物理研究，尤其是全核、高保真模拟代码的研究至关重要。确定性全核仿真工具总是依靠粗网格有限差分 (CMFD) 加速来实现快速收敛。然而，在通过 Picard 迭代耦合的多物理场问题中使用 CMFD 加速传输并不稳健，并且经常被松弛处理。在本文中，我们在之前使用傅立叶分析的理论工作的基础上，通过适当放松低阶扩散加速方程的收敛标准来证明如何在多物理场问题中实现稳定性和有效收敛。具体来说，我们开发了一种估计关键问题相关参数的方法，反馈强度，近最优部分收敛粗网格有限差分 (NOPC-CMFD) 方法所要求的。然后，我们描述了在密歇根并行特征传输 (MPACT) 代码中 NOPC-CMFD 的实现，并执行了一些数值计算。分析了从单个压水反应堆 (PWR) 燃料棒到全堆芯 PWR 循环耗尽的问题，以评估 NOPC-CMFD 在考虑多种形式的多物理场反馈的各种条件下的性能和稳健性。结果验证了我们配套论文的理论预测，说明 NOPC-CMFD 优于当前的 CMFD 或使用松弛的非线性扩散加速方案。总体而言，该方法能够在没有反馈的情况下在各种条件下恢复传统 CMFD 的性能。