适用于光厚、强散射介质的SN方程快速求解策略

为实现反应堆大厂房屏蔽问题的快速计算，需要建立一种能够尽可能减少数值负注量率、保证迭代格式的线性特性、同时能够在较大的网格内取得良好精度、计算量较小的离散纵标方法（SN）空间离散格式。本研究基于单群SN固定源输运方程的空间解析解，采用解析基函数展开方法实现SN空间离散；为了提高计算效率，采用权重系数方法，避免单个网格内大量的指数运算；研究高阶源项的计算方法，提高数值计算精度；最后基于Krylov子空间方法实现自散射源项的快速迭代计算。数值结果表明该方法可在材料区域较为均匀的光厚介质中取得较大的优势，可用于反应堆大厂房屏蔽问题的快速计算。 

A Scheme for Solving SN Equation on Optical Thick and Strong Anisotropic Scattering Medium

In order to realize fast calculation for the reactor facility shielding problem, it is necessary to establish a spatial discrete scheme for SN equation that can reduce the negative numerical flux, ensure the linearity of the iterative scheme, and achieve good accuracy in a large grid with minor calculation effort. This study is based on the spatial analytic solution of the within-group fixed source SN transport equation, and uses the analytic basis function method to expand the spatial term. In order to improve the calculation efficiency, the weighted coefficient method is used to avoid a large number of exponential operations in a single grid. High order source expansion is studied to improve the precision. Finally, a fast iterative scheme for the self-scattering source iteration is realized based on the Krylov subspace method. The numerical results show that this method can obtain great advantages in the optical thick medium with uniform material area, and can be used for the rapid calculation of shielding problem of large reactor building.