【摘要】 基于Galerkin有限元方法推导了多群中子扩散方程的变分形式，为解决控制棒尖齿效应问题，建立了控制棒尖齿效应修正模型，为解决定步长导致的计算时间较长问题，开发了自适应步长模型。采用C⁺⁺语言，基于开源多物理场面向对象仿真环境（multiphysics object oriented simulation environment, MOOSE）平台，开发了稳态、瞬态中子扩散程序Nurus＿diffusion。采用2维平板BSS3基准题、2维/3维IAEA基准题验证了程序求解特征值k_eff的功能；采用3维LMW基准题、2维TWIGL基准题验证了程序的瞬态求解功能。此外，在2维平板BSS3基准题中，还分析了网格规模的敏感性问题，在2维TWIGL基准题中分析了定步长与自适应步长对计算效率的影响。结果表明：Nurus＿diffusion程序求解特征值k_eff的偏差仅为2.8×10^-5（BSS3）、4×10^-4（IAEA）,LMW基准题、TWIGL基准题的瞬态相对功率最大偏差约为1.7%,结果与参考解符合较好；用稀疏网格计算时结果偏差较大，但随着网格量增加，计算精度迅速提高；采用自适应步长可在保证计算精度的基础上有效提高计算效率，但需要选择合适的步长权重因子。更多还原

【Abstract】 In this paper, the variational formulation of the multigroup neutron diffusion equation is derived based on Galerkin finite element method. Considering the control rod cusping phenomenon, a refined model is formulated. To counteract the protracted computational durations engendered by static temporal increments, an adaptive time-stepping schema is innovated. The steady state and spatial dynamics neutron diffusion code, Nurus＿diffusion is crafted in the C⁺⁺ language, ensconced within the Multiphysics object-oriented simulation environment（MOOSE） framework. The precision of the code in calculating eigenvalue k_eff is substantiated through the utilisation of the 2D BSS3 benchmark alongside the 2D/3D IAEA benchmark. The transient response capabilities of the code is corroborated via the 3D LMW benchmark and the 2D TWIGL benchmark. In addition, the impact of grid dimensionality on computational precision is analyzed in the 2D BSS3 benchmark. The impact of constant versus adaptive time-stepping on computational efficiency is analyzed in the 2D TWIGL benchmark. The results show that the deviation of eigenvalue k_eff calculated by the Nurus＿diffusion code are a mere 2.8×10^-5 for the BSS3 benchmark and 4×10^-4 for the IAEA benchmark. The maximal deviation of transient relative power for the LMW and TWIGL benchmarks is approximately 1.7%, demonstrating good agreement with the reference. The deviation of results is large when calculating with sparse grids. However, computational precision escalates significantly with the augmentation of grid density. Comparative analysis indicates that an adaptive time-stepping approach can substantially ameliorate computational efficiency without sacrificing accuracy, providing that an optimal weighting factor for the time-stepping selection is chosen.更多还原