非结构网格中子输运方程的球谐函数解法研究

从新的二阶自共扼角通量密度(SAAF：Self-Adjoint Angular Flux)中子输运方程出发．利用球谐函数对角度变量进行展开，导出了一组关于空间变量的偏微分方程组，中子通量密度的各个分量相互耦合，应用一定的迭代策略进行迭代求解。针对每一个方程，应用有限元方法对非结构网格进行离散求解。据此编写了二维球谐函数方法输运计算程序，对一系列基准题进行校算的数值结果表明，该方法具有较高的计算精度，克服了射线效应，并能用于非结构网格。

Spherical-Harmonics Method for Neutron Transport Equation Based on Unstructured-Meshes

The spherical harmonics method for neutron transport equation on unstructured-meshes is derived based on a new second order neutron transport equation, self-adjoint angular flux (SAAF) equation. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variables, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation code is programmed according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision result and avoid the ray effect very well.