中子输运方程的离散纵标-间断有限元数值模拟研究  

Numerical Simulation of S N-Discontinuous Finite Element Method for Neutron Transport Equation

作　　者：姜夺玉 张鹄 胡田亮 李达 江新标 许鹏 王立鹏 曹璐 张广春 JIANG Duoyu;ZHANG Hu;HU Tianliang;LI Da;JIANG Xinbiao;XU Peng;WANG Lipeng;CAO Lu;ZHANG Guangchun(National Key Laboratory of Intense Pulsed Radiation Simulation and Effect,Xi’an 710024,China;Rocket Force University of Engineering,Xi’an 710025,China;Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]强脉冲辐射环境模拟与效应全国重点实验室,西安710024 [2]火箭军工程大学,西安710025 [3]哈尔滨工业大学,哈尔滨150001

出　　处：《现代应用物理》2024年第6期27-34,共8页Modern Applied Physics

基　　金：国家自然科学基金资助项目(12205237,12275219)。

摘　　要：间断有限元方法可用来求解典型的中子输运方程。该方法无须在单元交界面处保持弱形式方程的连续性,因此在处理中子通量密度梯度较大的问题时,具有显著的精细化模拟能力。本文基于伽辽金间断有限元方法,结合离散纵标法推导了多群中子输运方程及其共轭方程的变分形式,并基于开源多物理场面向对象仿真环境平台MOOSE,开发了间断有限元格式的稳态中子输运程序Nurus_dgsn。该程序通用性较强,可以开展反应堆有效增殖因子、固定源问题、中子价值等重要参数的计算,并可以有效处理真空介质的中子输运问题。采用解析解问题、IAEA基准题、内真空固定源基准题、McCoy-Larsen基准题、共轭计算问题等算例对程序的通用性进行了验证。结果表明,对于解析解问题、共轭计算问题与IAEA基准题,特征值相对偏差最大约为0.042%;对于内真空固定源基准题和McCoy-Larsen基准题,平均中子通量密度最大相对偏差分别约为0.18%和-0.02%。The discontinuous finite element method(DFEM)epitomizes a quintessential strategy within finite element methodologies for addressing the neutron transport equation.This method is notably distinguished by its prerogative to forgo the necessity for continuity in the weak form equation across element interfaces,thereby rendering it exceptionally proficient for the intricate simulation of pronounced gradient variations in neutron flux.In this paper,the variational form of the multi-group neutron transport equation and its adjoint equation via the discrete-ordinates method are derived,utilizing the discontinuous Galerkin finite element method.Within the multiphysics object-oriented simulation environment(MOOSE)framework,a steady-state neutron transport code,named Nurus_dgsn is designed.This code is characterized by its formidable versatility,capable of calculating the reactor’s effective multiplication factor,addressing fixed source problems,determining neutron worth,among other critical parameters,while also adeptly managing neutron transport challenges within vacuum media.The code’s multifaceted capabilities are substantiated through a series of benchmark examples,including analytical benchmark,IAEA benchmark,internal vacuum fixed source benchmark,McCoy-Larsen benchmark,and adjoint calculation.Results show that the maximum relative deviation of k eff in comparison to the analytic solution,adjoint calculation,and IAEA benchmark is approximately 0.042%.Furthermore,the maximum deviation in mean neutron flux density between the internal vacuum fixed source benchmark and McCoy-Larsen benchmark is approximately 0.18%and-0.02%,respectively.

关 键 词：中子输运方程 离散纵标法 间断有限元 多物理场面向对象仿真环境(MOOSE) 

分 类 号：TL329[核科学技术—核技术及应用] O571[理学—粒子物理与原子核物理]