有限元SN中子输运模拟的区域分解并行

确定论中子输运方法具有计算速度快、可获取物理量的精细场分布、可高效多物理耦合等优点，随着有限元方法在中子输运模拟中的应用，复杂几何结构、大尺度下的屏蔽问题和临界问题都能得到高保真建模和分析。离散纵标（S_N）法是求解中子输运方程的有效数值方法，基于OpenMP并行机制对各独立离散方向进行并行求解，可提高S_N输运模拟的计算速度，但并行规模较有限。对几何空间进行区域分解并采用MPI并行机制，可实现大规模并行扩展，进而实现对大型问题的高精度快速求解。本文采用并行自适应非结构网格应用框架JAUMIN进行区域分解和进程间通信，通过并行S_N扫描实现了自主有限元输运程序ENTER的高效并行，完成正确性检验后在天河Ⅱ号超级计算机上使用1 440个CPU核完成了1.43×10⁷网格单元、2.81×10⁹自由度规模问题的测试，计算时间约7.4 h。表明该程序具备了有效模拟大型复杂结构中子输运问题的能力，具有一定工程应用价值。

Parallelization of Finite Element SN Neutron Transport Simulation Based on Domain Decomposition

The deterministic neutron transport method has the advantage of fast calculation speed, and is capable of giving fine field distribution of physical parameters and simulating multi-physics coupling efficiently. With the application of finite element method in neutron transport calculation, high fidelity modeling and simulation can be performed for complex geometric structures and large scale radiation shielding and criticality calculation. The discrete ordinate (S_N) algorithm is an efficient method in solving the Boltzmann neutron transport equation, and the parallelization of independent ordinate directions can be easily realized by the OpenMP scheme, but the speedup effect is limited by the number of discrete ordinate directions and the computation resources on single computer node or workstation. In order to improve the calculation speed further, the geometry domain decomposition method and the MPI parallel computing scheme can be applied to extend the parallel computing capability. The domain decomposition and communication between processes were accomplished by utilizing the parallel adaptive unstructured meshes applications infrastructure JAUMIN. And the parallelization of the formerly developed finite elementS_N neutron transport code ENTER was realized by implementing the parallelS_N sweeping algorithm. After verifying this parallel code on a workstation, several large scale problems on Tianhe-Ⅱ supercomputer with 1 440 CPUs were tested at most. The largest number of elements and degree of freedom were approximately 1.43×10⁷ and 2.81×10⁹, respectively, which cost simulation time of 7.4 h. The newly developed parallel neutron transport code ENTER has the capability of efficiently simulating large scale and complex geometry problems.