三维结构网格SN输运求解的指数短特征线空间离散方法

Exponential Short Characteristic Spatial Discretization Method for SN Transport Calculation on 3D Structured Grids

  • 摘要: 空间离散格式选取和空间网格划分对于离散纵标法求解粒子输运问题的计算精度至关重要。短特征线离散格式根据粒子出射、入射贡献关系分割计算网格,可有效消除因空间离散失真导致的非物理振荡问题。指数短特征线基于指数分布假设适合求解深穿透、强衰减的屏蔽问题,已有研究中变量代换处理过程存在几何运算冗余、非线性求解成本高等问题,影响计算效率和实际应用前景。本文基于三维结构网格提出新的指数短特征线离散格式,改变分割变换方案避免了单元投影映射过程,应用并调整指数矩算法、优化指数因子求解等处理改善计算效率。通过4个简单几何固定源问题定性定量比较分析了若干离散格式的计算精度与效率,指数短特征线方法粗网格精度远优于其他方法,出色的粗网格精度可补偿其较高的单网格计算成本,恰当的网格划分可发挥离散方法的计算效率。

     

    Abstract: Proper spatial discretization methods and mesh sizes are crucial for the computational accuracy of the discrete ordinates methods applied on the particle transport simulations. Short characteristic spatial discretization splits the computational cell based on the relationship between incoming and outgoing particles, and is capable of mitigating non-physical oscillations caused by the deficiency of the spatial variable discretizing. Exponential short characteristic (EC) is suitable for shielding problems with deep-penetration and strong attenuation, but there are expensive numerical processes including the redundant geometric calculation and nonlinear solving in the previous studies. A modified EC scheme was developed based on 3D structured grids, and the projection mapping was avoided by applying the new splitting-substituting scheme. Optimized exponential moment and exponential factor solving algorithms improve the computational efficiency. From results of four fixed-source problems with simple geometry, accuracy and efficiency were compared among several spatial schemes. The accuracy of EC on the coarse meshes is much better than that of other methods, and its excellent coarse mesh accuracy is cable of compensating the expensive computational cost. Proper mesh distributions help to realize the EC’s advantage of the computational efficiency.

     

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