角度自适应离散纵标输运计算方法

精确的屏蔽计算方法是核装置辐射屏蔽设计的重要基础，离散纵标法(SN)是主要的屏蔽计算方法之一。本文基于价值理论的目标导向与角度自适应相结合的方法，有效地减弱了角度的离散误差。求解输运共轭方程获得目标函数的重要性分布，采用局部角度离散误差与目标函数的重要性加权，产生后验误差估计，为角度自适应过程提供判断依据。角通量密度的映射采用多项式权重法和球谐函数拟合法。数值结果表明，对于具有直孔道或曲折孔道的屏蔽问题，在相同精度下离散角度数减少了1～2个数量级，极大地减少了计算量。角度自适应方法以较少的离散方向获得了准确的计算结果，有效地减弱了角度离散误差对屏蔽计算精度的影响。

Angular Adaptive Discrete Ordinates Method for Transport Equation

Accurate shielding calculation method is an important foundation of shielding design of nuclear system. Discrete ordinates method (SN) is one of the main shielding calculation methods. An angular adaptive algorithm together with a goal oriented error estimate was proposed to eliminate the angular discretization errors. The importance of the objective function was obtained by solving the adjoint transport equation. Local angular discretization errors were weighted by the importance of a given angular region toward the computational goal, providing an appropriate goal oriented angular adaptivity. The mapping schemes were applied to the transition of angular flux solution between adjacent spatial regions with different quadrature sets during the source iteration process. The numerical results demonstrate that at the same accuracy, the number of angular discretization is reduced by 1-2 orders for shielding problems with straight or zigzag channels and the amount of computation is greatly reduced. The adaptive method generates the most effective discrete angle distribution and eliminates the influence of angular discretization errors on the shielding calculation.