三维斜流线性完全耦合层吸收边界条件

中国机械工程 ›› 2015, Vol. 26 ›› Issue (1): 1-7.

三维斜流线性完全耦合层吸收边界条件

伍新1,2;陈志夫3;尹汉锋1

1.湖南大学汽车车身先进设计制造国家重点实验室，长沙，410082
2.湖南工程学院，湘潭，411104
3.广州汽车集团股份有限公司汽车工程研究院，广州，511434

出版日期:2015-01-10 发布日期:2015-01-15
基金资助:
国家自然科学基金资助项目（11302075,11002052）；湖南省教育厅高等学校科学研究项目（12C0627）

Three Dimensional Linear PML Absorbing Boundary Conditions with an Oblique Mean Flow

Wu Xin1,2;Chen Zhifu3;Yin Hanfeng1

1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082
2.Hunan Institute of Engineering,Xiangtan,Hunan,411104
3.Guangzhou Automobile Group Co.,Ltd. Automotive Engineering Institute,Guangzhou,511434

Online:2015-01-10 Published:2015-01-15
Supported by:
National Natural Science Foundation of China（No. 11302075,11002052）

摘要/Abstract

摘要：

采用傅里叶与拉普拉斯变换方法分析了三维斜流背景下声波、涡波与熵波的色散关系;根据各物理波的色散轨迹特征，结合频率变化的时空坐标变换方法，给出了一组时间与空间坐标变换关系式，并将三维斜流线性欧拉方程变换至新坐标系;采用复数变换方法，引入阻尼，分别构建了x层、y层、z层及角层的完全耦合层（PML）吸收边界条件,给出了吸收项的施加原则;最后通过三维脉冲声波、对称涡环与周期性点声源在斜时均流中的传播问题验证了该吸收边界条件的正确性。研究结果表明：所提出的坐标变换关系能够有效解决各物理波相位速度与群速度不一致的问题;在斜背景流下，该PML吸收边界条件能较好地吸收物理波，有效抑制边界反射，可用于气动声学计算。

关键词: 完全耦合层, 边界条件, 计算气动声学, 欧拉方程, 色散

Abstract:

For three dimensional linear Euler equations in the case of oblique mean flow, the dispersion relations of acoustic, vortex and entropy wave were first analyzed by using Fourier and Laplace transform method. Then the hypothesis for changed frequency was employed, a proper space-time transformation was presented for deriving three dimensional linear Euler equations in transformed coordinates. A complex change was applied to the new equations and a damping parameter was introduced. A three linear PML absorbing boundary conditions in the case of oblique mean flow for x layer, y layer, z layer and corner layer were derived. In addition, the importance of added absorption term was emphasized. Finally, the effectiveness of linear PML absorbing boundary conditions was validated by computing the computational aeroacoustics benchmark problems. The results prove that: the presented space-time transformation can solve the problem of direction inconsistence in group and phase velocity of physical wave; in the case of oblique mean flow, the proposed PML absorbing boundary conditions can absorb the physical wave with little or no reflection.Therefore,it also can be applied to aeroacoustic computation.

Key words: perfectly matched layer(PML), boundary condition, computational aeroacoustics, Euler equation, dispersion

中图分类号:

V211.3

伍新, 陈志夫, 尹汉锋. 三维斜流线性完全耦合层吸收边界条件[J]. 中国机械工程, 2015, 26(1): 1-7.

Wu Xin, Chen Zhifu, Yin Hanfeng. Three Dimensional Linear PML Absorbing Boundary Conditions with an Oblique Mean Flow[J]. China Mechanical Engineering, 2015, 26(1): 1-7.

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