北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (3): 551-561.doi: 10.13700/j.bh.1001-5965.2015.0197

• 论文 • 上一篇    下一篇

适用于混合网格的改进雅可比迭代法及其应用

黄宇1, 阎超1, 袁武2   

  1. 1. 北京航空航天大学航空科学与工程学院, 北京 100083;
    2. 中国科学院计算机网络信息中心超级计算中心, 北京 100190
  • 收稿日期:2015-04-07 出版日期:2016-03-20 发布日期:2016-03-25
  • 通讯作者: 阎超,Tel.:010-82317019 E-mail:yanchao@buaa.edu.cn E-mail:yanchao@buaa.edu.cn
  • 作者简介:黄宇 男,博士研究生。主要研究方向:计算流体力学、混合网格数值方法。Tel.:010-82338071 E-mail:huangyu@buaa.edu.cn;阎超 男,博士,教授,博士生导师。主要研究方向:计算流体力学、空气动力学。Tel.:010-82317019 E-mail:yanchao@buaa.edu.cn

Improved Jacobi iterative method for hybrid grid and its application

HUANG Yu1, YAN Chao1, YUAN Wu2   

  1. 1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. Super Computing Center, Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2015-04-07 Online:2016-03-20 Published:2016-03-25

摘要: LU-SGS因有较高的鲁棒性和小的内存需求而得到广泛应用,然而用于混合网格计算前需要进行网格排序和分组来实现算法并行;此外,LU-SGS格式收敛效率不高。针对这些缺点,本文提出了一种改进的适用于复杂混合网格的雅可比迭代方法,无需网格排序和分组就可实现算法的并行化,且有较快的收敛速度。该方法编程实现简单,易于采用OpenMP实现并行。算例研究表明,相比于LU-SGS格式,在各来流条件下,本文提出的方法收敛速度更快,鲁棒性好,并行和串行结果一致,且内存需求增加很少。

关键词: 混合网格, 隐式算法, 并行计算, OpenMP, 雅可比迭代, 网格排序

Abstract: LU-SGS scheme is widely used today because of its robustness and cheap memory cost. However, the original LU-SGS shows less competitive convergence rate; in order to apply paralleled codes on hybrid unstructured grid, the grid reordering and regrouping procedure must be carried out beforehand. In this paper, an improved implicit method suitable for complex hybrid gird is developed to achieve fast convergence rate and to parallelize the algorithm without grid reordering and regrouping procedure. This method is simple for coding and easy to use OpenMP for code parallelization. The numerical results of Euler and viscous flows show that the method has a reliable performance, and it is able to achieve a significant efficiency improvement over implicit counterparts such as LU-SGS scheme with less requirement of extra memory, and parallel computation produce exactly the same result as serial case.

Key words: hybrid grid, implicit method, parallel computation, OpenMP, Jacobi iteration, grid reorder

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