Finite difference method for 3D multi-group neutron diffusion equation based on large-scale parallel computation
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摘要: 三维多群中子扩散方程的精确、高效求解是核动力堆芯设计及燃料管理的基础。应用有限差分方法求解该方程具有简便、精确、成熟的优点；然而,该方法的计算量和存储量均较大,极大地限制了它的计算规模和应用范围。本文基于大规模并行计算,研究三维多群中子扩散方程有限差分方法：采用中心有限差分格式离散中子扩散方程；基于MPI并行编程模型,采用空间区域分解的方式实现大规模并行计算；采用多群多区域耦合PGMRES算法进行并行加速。在集群服务器上开发了ParaFiDi程序,并采用IAEA3D,PHWR等多个基准题对该程序进行验证。数值结果表明,ParaFiDi程序具有较高的计算精度和计算效率。
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关键词:
- 三维多群中子扩散方程 /
- 有限差分方法 /
- 大规模并行计算 /
- 区域分解算法 /
- 多群多区域耦合PGMRES算法
Abstract: Nuclear design and fuel management of submarine reactors and NPP reactors are based on solving 3D multi-group neutron diffusion equation accurately and efficiently. One of the methods for this equation is finite difference method (FDM), which is simple, accurate and mature. However, the computation burden of FDM is huge and the memory requirement is high, thus limiting FDMs scale and application scope. In this paper, FDM for 3D multi-group neutron diffusion equation based on large-scale parallel computation is researched. Mesh-centered FDM is used to discrete the neutron diffusion equation. Large-scale parallel computation is realized by domain decomposition based on MPI, and its accelerated with multi-group multi-domain coupled PGMRES algorithm. ParaFiDi code is developed on high performance cluster and verified by several benchmarks such as IAEA3D and PHWR. Numerical results demonstrate that ParaFiDi code could obtain good efficiency and accuracy. -
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