二维中子输运问题的离散纵标短特征线方法研究

离散纵标法是求解中子输运方程的主要数值方法之一，空间变量离散及误差控制对保证输运计算精度至关重要。传统有限差分离散方法对于特定模型会产生非物理振荡问题，粗网精度不足使得低阶差分方法的应用具有局限性。本文研究了二维常数和线性短特征线方法，短特征线空间离散基于中子输运的特征线解，根据输运方程的空间矩守恒构造网格角通量密度完成输运方程求解。选取固定源和临界问题进行测试验证并分析了网格敏感性。数值结果表明，线性短特征线离散对网格敏感性较低，较常数短特征线和低阶差分方法具有更高的计算精度及效率。

Discrete Ordinates Method with Short Characteristic Spatial Discretization for Neutron Transport Problem in 2D Geometry

Discrete ordinates method is one of main numerical methods for solving neutron transport equation, and spatial discretization and its error control are essential for computational accuracy. Traditional finite difference methods possess unphysical oscillations for specific circumstances and inaccuracy under coarse meshes limits their application. Step and linear short characteristic methods for the S_N equation were proposed. Short characteristic methods construct angular flux distribution based on characteristic solution according to spatial moment conservation of transport equation. Numerical verification and sensibility analysis about mesh size were conducted. Results of short characteristic method are in good agreement with the references. Results indicate that linear short characteristic scheme is less sensitive to mesh size and gains better accuracy over step short characteristic and other low-order difference methods.