三维中子输运方程的非结构网格离散纵标数值解法

从一阶三维中子输运方程出发，对方向变量采用离散纵标方法展开，得到一系列关于空间变量的偏微分方程，从而避免了二阶方程由于分母上存在截面，不能准确描述内含真空介质的问题．对这些关于空间变量的方程采用最小二乘有限元方法进行离散，形成的刚度矩阵是对称的，因此可以采用快速迭代方法求解．据此编制了三维中子输运方程的非结构网格离散纵标计算程序，并采用三棱柱元素和四面体元素剖分对一系列基准问题做了验算．计算结果表明，该方法能用于非结构网格，并具有较高的计算精度，对多数问题，有效增值系数的误差都小于0．3％，通量误差都小于3．0％．

Discrete Ordinates Method for Three-Dimensional Neutron Transport Equation Based on Unstructured-Meshes

A discrete ordinates method for three-dimensional neutron transport equation based on unstructured-meshes was derived from the first-order neutron transport equation. A set of differential equations about the spatial variables were obtained. It avoids the singularity in void regions from the second-order form of the equation, which implies the inversion of the total cross-section. The differential equations were solved iteratively using the least-squares finite element method. For the symmetric stiffness matrix, the fast iteration method can be used. A three-dimensional transport calculation code was programmed. The triangular prism and the tetrahedron elements were used in the calculation. The numerical results of some benchmark problems show that this method can be used in unstructured-meshes and can give high precise result. For most problems, the error is less than 0. 3% for the eigenvalue and 3.0% for the angular flux, respectively.