An optimized sweeping solution method for the three-dimensional Sn equations of neutron transport on hexahedral meshes
An optimized sweeping solution method for the three-dimensional Sn equations of neutron transport on hexahedral meshes
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DOI：
10.1016/j.jcp.2022.110964
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发表时间：
2022-01
期刊：
影响因子：
--
通讯作者：
Ya-Jun Gao;Xudeng Hang;G. Yuan
中科院分区：
文献类型：
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作者：
Ya-Jun Gao;Xudeng Hang;G. Yuan
本文提出了一种新的在一般六面体网格上求解中子输运三维离散纵坐标方程的扫描求解方法，重点讨论了表面积分和扫描死锁的处理.本文的主要贡献包括三个方面。首先，采用有效面法对非平面单元面上的曲面积分进行离散，在不分解单元面的情况下成功地解决了重入问题。其次，基于有效面方法，我们设计了一个新的排序算法，适用于任意六面体网格。该算法避免了依赖环的识别，并在选择用于消除扫描死锁的滞后单元时考虑了传输问题的物理特性。结合上述改进，提出了一种在一般六面体网格上求解Sn方程的分裂扫描迭代法。最后，从理论上证明了这种扫描迭代法总是收敛的，解耦方法对迭代收敛速度的影响很小。数值实验表明，所提出的方法的有效性的立方和球面域。本文提出的方法同样适用于多面体网格或二维多边形网格。
We propose a new sweeping solution method for the three-dimensional (3D) discrete ordinates (Sn) equations of neutron transport on general hexahedral meshes, with particular focus on handling the surface integrals and sweeping deadlocks. The main contributions of this paper include three aspects. Firstly, the surface integrals on the non-planar cell faces are well discretized by virtue of the effective face method, which successfully addresses the reentrance problem without the decomposition of the cell faces. Secondly, based on the effective face method, we devise a new sorting algorithm which works for any hexahedral meshes. In this algorithm, the identification for dependent cycles is avoided and the physical characteristics of transport problems are taken into account in the choice of lagged cells used to decouple the sweeping deadlocks. Combining the above advancements, a splitting sweeping iterative method is proposed for the solution of the Sn equations on general hexahedral meshes. Finally, we prove theoretically that this sweeping iterative method always converges, and the decoupling method affects little on iterative convergence rate. Numerical experiments are presented to demonstrate the effectiveness of the proposed methods on both cubic and spherical domains. The ideas presented in this paper are also applicable to the polyhedral meshes or two-dimensional polygonal meshes.