球谐函数有限元程序NECP-FISH的开发及其在聚变堆包层中子学分析中的应用

球谐函数有限元方法采用非结构网格求解中子输运方程，具备处理复杂几何的能力；同时又可避免离散纵标方法所造成的射线效应。本文从一阶中子输运方程出发，通过方程的弱形式推导了球谐函数多尺度有限元方法，并基于此方法开发了中子学分析程序NECP-FISH。通过在前后处理平台SALOME中开发接口程序，实现了程序的建模可视化和计算结果可视化。应用此程序计算了氦冷陶瓷包层，数值结果表明NECP-FISH对中子通量密度、氚增殖比和中子释热的计算结果与蒙特卡罗程序NECP-MCX吻合良好。氚增殖比相对偏差为0.56%，所有区域的中子释热偏差均在6%以内。

Development of Spherical Harmonic Finite Element Code NECP-FISH and Its Application in Neutronics Analysis of Fusion Reactor Blanket

The spherical harmonic finite element method is used to solve the neutron transport equation with unstructured meshes, which has the ability to deal with complex geometry and can avoid the ray effect caused by discrete ordinate method. The spherical harmonic multi-scale finite element method was derived from the weak form of the first-order transport equation. A neutronics analysis code NECP-FISH was developed based on the derived method. Through the developed interface program in SALOME, the visual modeling and results visualization were realized. Finally, this program was used to calculate helium cooled ceramic blanket. The neutron flux density, tritium breeding ratio (TBR) and nuclear heating calculated by NECP-FISH are in good agreement with those of Monte Carlo code NECP-MCX. The relative deviation of TBR is 0.56% and the nuclear heating deviations of all regions are less than 6%.