旋转坐标系下分区计算的LU隐式方法

doi:10.7527/S1000-6893.2018.22079

流体力学与飞行力学

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旋转坐标系下分区计算的LU隐式方法

肖中云, 刘刚, 牟斌, 江雄

中国空气动力研究与发展中心计算空气动力研究所, 绵阳 621000

收稿日期:2018-02-04 修回日期:2018-06-11 出版日期:2018-10-15 发布日期:2018-06-21
通讯作者: 牟斌 E-mail:809970229@qq.com
基金资助:
国家重点研究发展计划（2016YFB0200701）；国家自然科学基金（11572341）

LU implicit methods for partitioned computation in rotating coordinate system

XIAO Zhongyun, LIU Gang, MOU Bin, JIANG Xiong

Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Received:2018-02-04 Revised:2018-06-11 Online:2018-10-15 Published:2018-06-21
Supported by:
National Key Research and Development Program (2016YFB0200701); National Natural Science Foundation of China (11572341)

摘要/Abstract

摘要： 将隐式时间迭代方法应用于并行计算是CFD研究中的热点问题，研究发现LU-SGS格式在旋转坐标系下对分区边界比较敏感，对旋翼悬停状态进行分区并行计算时碰到了计算发散的问题。针对此问题，对基于LU分解的3种隐式时间迭代格式（LU-SGS、DP-LUR和HLU-SGS）进行了对比研究，设计了静止流场下的旋转网格算例对计算方法进行测试。结果表明，LU-SGS格式在网格边界采用简化处理方法，当边界的逆变速度增大时会引起数值误差放大，误差的不断积累导致计算发散。DP-LUR和HLU-SGS格式通过在边界单元采用雅克比迭代算法，能有效消除分区边界影响，使计算格式在大CFL数条件下保持稳定，其中HLU-SGS继承了LU-SGS迭代效率高的特点。在此基础上，采用并行化的LU隐式方法对Caradonna-Tung旋翼进行了并行计算，针对两套稀密程度不同的背景网格，在产生复杂分区边界的计算网格条件下，均获得了气动力和旋翼尾迹都充分收敛的流场。通过计算，分析了背景网格密度对预测气动力性能和捕捉尾迹流场的影响，计算结果与试验值吻合良好，验证了当前隐式计算方法适用于旋转坐标系并行计算，适合于推广至其他大规模并行分区的流场计算。

关键词: 隐式方法, LU分解, 并行计算, 分区计算, 旋翼

Abstract: The application of implicit time iterative method to parallel computing is a hot issue in CFD research. It is found that LU-SGS scheme is sensitive to partition boundary in the rotating reference frame, and thus the problem of computational divergence is encountered in parallel calculation of the hovering rotor. To solve this problem, three implicit time iterative schemes based on LU decomposition (namely LU-SGS, DP-LUR, and HLU-SGS) are studied comparatively, and a rotating grid example is designed to test these calculation methods. Results show that as the LU-SGS scheme uses a simplified method to deal with boundary cells, numerical errors increases in proportion to the rotating speed and accumulation of errors leads to divergence of calculation. DP-LUR and HLU-SGS schemes can effectively eliminate the influence of partition boundaries by using Jacobian iterations in boundary cells, and both keep the scheme stable with large CFL number. HLU-SGS inherits the high efficiency of LU-SGS scheme. Parallel computations of the Caradonna-Tung rotor are then carried out by the three schemes, where coarse and fine background meshes are studied comparatively. Although complex partition boundaries are produced for parallel computation, fully converged results of the aerodynamic force and wake are obtained. The computation results are in good agreement with experimental data, showing that current implicit time stepping methods are applicable for parallel computation in rotating reference frame, and can be furtherly extended to other large scale parallel computations.

Key words: implicit algorithm, LU decomposition, parallel computation, partition computation, rotor

中图分类号:

V211.3

肖中云, 刘刚, 牟斌, 江雄. 旋转坐标系下分区计算的LU隐式方法[J]. 航空学报, 2018, 39(10): 122079-122079.

XIAO Zhongyun, LIU Gang, MOU Bin, JIANG Xiong. LU implicit methods for partitioned computation in rotating coordinate system[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(10): 122079-122079.

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E-mail：hkxb@buaa.edu.cn

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旋转坐标系下分区计算的LU隐式方法

LU implicit methods for partitioned computation in rotating coordinate system

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