基于CAD建模和有限元方法的三维中子扩散程序

3-D neutron diffusion code based on CAD preprocessing and the finite element method

有限元方法(finite element method,FEM)适应于复杂几何问题的数值计算,但目前反应堆物理有限元程序所采用的前处理(即几何建模和网格划分)方法繁琐抽象,较难应用于高维复杂结构。该文通过采用计算机辅助设计(computer aided design,CAD)商业软件GAMBIT进行可视化自动建模和网格划分,并应用于自主开发的有限元三维中子扩散程序FEMND,实现了对高维复杂堆芯的直接准确模拟。该程序系统对二维和三维几何分别采用非结构三角形和四面体网格划分,采用不完全LU分解预优共轭梯度法求解代数方程组,可处理临界和含外源问题。通过多个理论模型和基准问题验证了程序的可靠性和正确性,表明有限元方法与CAD前处理相结合,可以充分发挥有限元方法的优势,实现对复杂结构堆芯的有效模拟。

The finite element method （FEM） has advantages for analyzing complex geometry; however, the preprocessing used in finite element codes for nuclear reactor physics is tedious, complicated and not convenient for high dimensional cases. This paper describes an automatical modeling and meshing method using a graphical interface based on the commercial computer aided design （CAD） software GAMBIT. The system is used in a three-dimensional neutron diffusion code, FEMND, to simulate complex reactor cores. This code uses unstructured triangular and tetrahedral elements for two and three dimensional problems, with the incomplete I.U factorized conjugate gradient （ILUCG） algorithm used to solve the algebraic equations. Both critical and external source driven problems can be simulated. The code has been verified with several benchmarks. This code combines the finite element