解析基函数展开方法求解二维三角形几何中子扩散方程

Analytic Basis Function Expansion Method for Neutron Diffusion Calculation in Two-Dimensional Triangular Geometry

提出了一种在二维三角形几何内数值求解中子扩散方程的节块方法。节块内的各群通量分布用解析基函数近似展开,节块之间采用面偏流零次矩和一次矩进行耦合;给出了三角形几何下的节块扫描方案;采用响应矩阵技术进行迭代求解,开发了二维三角形组件中子扩散计算程序ABFEM-T。通过基准问题的校验计算,表明该方法能准确地给出有效增值系数及节块功率分布,可用于复杂的非结构几何区域的中子扩散问题的求解。

A new nodal method for directly solving the two-group neutron diffusion equation in the triangular geometry was proposed. The neutron flux distributions within a node were expanded in a series of analytic basis functions for each group. Nodes were coupled each other with both the zero-and fin＇st-order partial neutron current moments simultaneously. With a new sweeping scheme developed for triangular geometry, the response matrix technique was used to solve the nodal diffusion equations iteratively. Based on the proposed model, the code ABFEM-T was developed. The numerical results for a series of benchmark problems show that the core multiplication factor and nodal powers are predicted accurately using this model for unstructured neutron diffusion problems.