二维稳态辐射声场的光滑有限元-完美匹配层解法

夏百战; 于德介; 姚凌云

doi:10.6052/0459-1879-2012-2-20120232

二维稳态辐射声场的光滑有限元-完美匹配层解法

湖南大学汽车车身先进设计制造国家重点实验室, 长沙 410082

基金项目: 国家高技术研究发展计划资助项目(2009AA04Z414).

详细信息

中图分类号: TB532
计量
- 文章访问数: 1569
- HTML全文浏览量: 57
- PDF下载量: 801
出版历程
- 收稿日期: 2011-07-25
- 修回日期: 2011-11-03
- 刊出日期: 2012-03-17

A SMOOTHED FINITE ELEMENT-PERFECTLY MATCHED LAYER METHOD FOR TWO-DIMENSIONAL STEADY-STATE RADIATION ACOUSTIC FIELD PROBLEMS

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China

Funds: The project was supported by the the National High Technology Research and Development Program of China (2009AA04Z414).

摘要

摘要: 针对外场声学有限元计算精度偏低的问题, 将光滑有限元技术引入到二维稳态辐射声场预测中, 提出了光滑有限元-完美匹配层解法. 该解法采用完美匹配层截断声场计算域, 并将其离散为等参四边形单元, 采用指数吸收函数实现完美匹配层内参数坐标和笛卡尔坐标的映射关系, 采用光滑声压梯度技术计算辐射声场刚度矩阵, 将形函数梯度的域内积分转换为形函数域边界积分. 某汽车二维声腔辐射声场的数值分析结果表明, 与标准有限元-完美匹配层相比, 光滑有限元-完美匹配层解法在完美匹配层内的声波吸收效果更好, 在计算域内的数值计算精度更高, 具有良好的工程应用前景.
- Helmholtz方程 /
- 光滑有限元 /
- 完美匹配层 /
- 辐射声场
Abstract: Aiming at the problem of low accuracy of finite element method (FEM) for exterior acoustics analysis, the smoothed finite element method- perfectly matched layer (SFEM-PML) method is proposed for the analysis of two-dimensional steady-state acoustic radiation problem. In SFEM-PML, the computational region, truncated by perfectly matched layer(PML), is discreted into four-node isoparametric elements. The mapping relation between the PML's parameter coordinates and Cartesian coordinates is implemented by using the exponential absorbing function. In order to recast the domain integrals involving shape function gradients to the boundary integrals involving only shape functions，the radiant acoustic stiffness matrix is calculated by using the smoothed acoustic pressure gradient matrix. Numerical example of a two-dimensional radiation field of acoustic cavity of automobile is presented，which shows that SFEM-PML achieves better absorbing effect in PML, and higher accuracy in the computational region as compared with FEM-PML. Hence the SFEM-PML can be well applied in solving two dimensional acoustic radiation problems, and has a wide application foreground.
- Helmholtz equation /
- smoothed finite element method /
- perfectly matched layer /
- radiation acoustic field

HTML全文

参考文献(9)

1 Engquist B, Majda A. Absorbing boundary conditions for thenumerical simulation of waves. it Math Comput, 1977, 31(139): 629-651

2 Givoli D. High-order local non-reflecting boundary conditions: a review. it Wave Motion, 2004, 39(4): 319-326

3 Berenger JP. A perfectly matched layer for the absorption of electromagnetic waves. it J Comput Phys, 1994, 114(1): 185-200

4 Hohaga T, Schmidt F, Zschiedrich L. Solving time-harmonic scattering problems based on the pole condition. II: Convergence o f the PML method. it SIAM J Math Anal, 2004, 35(3): 547-560

5 Shirron JJ, Giddings TE. A finite element model for acoustic scattering from objects near a fluid-fluid interface. it Comput Methods Appl Mech Engrg, 2006, 196(1-3): 279-288

6 Bermúdez A, Hervella-Nieto L, Prieto A, et al. An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. it J Comput Phys, 2007, 223(2): 469-488

7 Liu GR, Nguyen TT, Dai KY, et al. Theoretical aspects of the smoothed finite element method (SFEM). it Int J Numer Meth Engng, 2007, 71(8): 902-930

8 Yao LY, Yu DJ, Zang XG. Numerical treatment of acoustic problems with the smoothed finite element method. it Appl Acoust, 2010, 71(8): 743-753

9 Rejlek J, Pluymers B, Diwoky F, et al. Validation of the wave based technique for the analysis of 2D steady-state acoustic radiation problems. In: Proceeding of International Conference on Engineering Dynamics Location, Algarve, Portugal, 2007. 6-18