核反应堆三维模拟的高分辨率高效率非均匀中子输运计算方法研究

With the growing quest for higher economy and safety of nuclear reactors, the traditional neutronics method that performs multi-level homogenization and low-order approximations can hardly satisfy the requirement of enhancing accuracy. As a result, in recent years high-fidelity techniques have been widely pursued in nuclear reactor three-dimensional simulations. Due to the probability mechanism or multi-dimensional coupled iteration algorithm, existing high-fidelity techniques have been challenged by problems of low efficiency, pseudo-convergence or even divergence. In this proposal, we propose an innovative approach which deals with the challenges rooted in existing high-fidelity methods. This method is characterized by three-dimensional whole-core heterogeneous neutron transport calculations with high resolution and high efficiency. Leveraging the heterogeneous variational principal, this method will be established on the direct three-dimensional transport solution of the reactor core model with high resolutions, whereby avoiding the convergence problems and accuracy problems caused by multi-dimensional coupled iterations. Moreover, the integral transport technique and the numerical optimization algorithm will be adopted to accelerate the formation of response matrices. Last but not least, advanced parallelization algorithms based on domain-decomposition will be implemented and optimized to solve the resulting matrix equations efficiently, thus ensuring the feasibility for industry use. It is believed that this cutting-edge research will not only constitute an advancement of the neutron transport theory, but also provide a practical technique for reactor design and safety analysis.

为了保障核反应堆的经济性和安全性，基于多级均匀化和低阶假设的传统中子学计算方法已经难以满足提升计算精度的需求，先进的高保真中子学计算方法逐步成为核反应堆三维模拟的研究热点。现有的高保真中子学计算方法多基于概率统计机制或多维耦合迭代算法，受到效率低、伪收敛甚至不收敛等问题的挑战。本研究针对以上难题提出了新思路，拟开展高分辨率、高效率的三维全堆芯非均匀中子输运计算方法研究。本方法基于非均匀变分原理，拟在严格输运理论下实现高分辨率核反应堆模型的直接三维中子输运求解，能够避免多维耦合迭代导致的难收敛和低精度问题；拟建立积分输运技术和数值优化算法，加速响应矩阵的计算；拟基于区域分解探究和对比不同的并行算法，提高矩阵方程的求解效率，以保障拟建立方法的工程实用性。本研究不仅对于中子输运理论的发展有着重要的科学意义，而且在反应堆的堆芯设计和安全分析中有着广泛的应用前景，属于前沿性的基础研究。

为了保障核反应堆的经济性和安全性，基于多级均匀化和低阶假设的传统中子学计算方法已经难以满足提升计算精度的需求，先进的高保真中子学计算方法逐步成为核反应堆三维模拟的研究热点。现有的高保真中子学计算方法多基于概率统计机制或多维耦合迭代算法，受到效率低、伪收敛甚至不收敛等问题的挑战。本研究针对以上难题提出了新思路，开展高分辨率、高效率的三维全堆芯非均匀中子输运计算方法研究。基于非均匀变分原理，在严格输运理论下实现高分辨率核反应堆模型的直接三维中子输运求解，针对三维C5G7问题的模拟keff误差低于150pcm，积分棒功率偏差低于0.5%；建立了RCMK数值优化方法，将响应矩阵转换为带状分块矩阵，大大降低响应矩阵的计算时间；开发了广义PM加速方法，获得了由于CMFD的计算稳定性，并将pin-by-pin问题的外迭代次数降低70%以上。结合粗网加速算法，可以实现12.5倍的加速比；基于区域分解开发了红黑迭代并行算法，提高矩阵方程的求解效率，百核以上并行效率大于90%。此外，还拓展性地将本项目所开发的一系列算法应用于均匀节块问题的中子输运方程的求解：针对六角形几何节块，建立了基于全三维输运的准反射边界条件角度加速算法，加速比高于6.7倍；针对矩形几何节块，建立了基于2D/1D思想的准输运方法，在保证计算进度的同时，降低了降低 75%的计算内存，减少 93%的计算时间，提升了中子输运方法应用于工程规模问题的可行性。本研究不仅对于中子输运理论的发展有着重要的科学意义，而且在反应堆的堆芯设计和安全分析中有着广泛的应用前景。

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