现代应用物理2024，Vol.15Issue(3)：20-29,44,11.DOI:10.12061/j.issn.2095-6223.2024.030202
基于MOOSE平台的中子扩散方程数值解法
Numerical Solution of Neutron Diffusion Equation Based on MOOSE Framework
摘要
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 keff 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 eigenvaluekeffcalculated 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.关键词
中子扩散方程/Galerkin有限元法/MOOSE/Nurus_diffusionKey words
Neutron diffusion equation/Galerkin finite element method/MOOSE/Nurus diffusion分类
能源科技引用本文复制引用
姜夺玉,许鹏,胡田亮,江新标,王立鹏,曹璐,李达,陈立新..基于MOOSE平台的中子扩散方程数值解法[J].现代应用物理,2024,15(3):20-29,44,11.基金项目
国家自然科学基金资助项目(12205237,12275219) （12205237,12275219）
