亚音速均匀流场中无限域声传播模拟的快速奇异边界法

廖琪琦; 习强; 徐文志; 傅卓佳

doi:10.21656/1000-0887.450339

亚音速均匀流场中无限域声传播模拟的快速奇异边界法

doi: 10.21656/1000-0887.450339

河海大学力学与工程科学学院，南京 211100

我刊青年编委傅卓佳来稿

基金项目:

国家自然科学基金 12122205

国家自然科学基金 12372196

国家自然科学基金 12302258

详细信息

作者简介:
廖琪琦(2001—)，女，硕士生(E-mail: 221308010054@hhu.edu.cn)

通讯作者:
傅卓佳(1985—)，男，教授，博士生导师(通讯作者. E-mail: paul212063@hhu.edu.cn)

中图分类号: O302
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- 文章访问数: 50
- HTML全文浏览量: 12
- PDF下载量: 13
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-24
- 修回日期: 2025-03-30
- 刊出日期: 2025-06-01

A Fast Singular Boundary Method for Simulation of Infinite-Domain Acoustic Propagation in Subsonic Uniform Flow

College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, P.R.China

Contributed by FU Zhuojia, M.AMM Youth Editorial Board

摘要

摘要: 快速奇异边界法被首次用于求解亚音速均匀流场中的无限域声传播问题. 在奇异边界法中，满足亚音速均匀流场中声传播特性的基本解与权重系数的线性组合被用于计算得到声压. 其中，源点强度因子被用于解决基本解的源点奇异性问题，基于递归骨架分解技术的快速直接求解法被用于分解压缩奇异边界法在大规模声学计算中生成的稠密矩阵. 最后，在两个数值算例中，通过与解析解、有限元参考解及已有文献结果的对比验证了快速奇异边界法的精确性、收敛性和有效性，并且探究了Mach数、波数对亚音速均匀流场中声传播的影响.
- 奇异边界法 /
- 快速算法 /
- 亚音速均匀流 /
- 无限域 /
- 声传播
Abstract: The fast singular boundary method was employed to simulate acoustic propagation in infinite domains under subsonic uniform flow. In this approach, a linear combination of the fundamental solutions satisfying the acoustic propagation properties in subsonic flow and the weighting factors was used to compute the sound pressure. The origin intensity factors were used to resolve the singularity of the fundamental solution. A fast direct method, based on recursive skeleton decomposition, was applied to compress the dense matrices generated with the singular boundary method for solving large-scale acoustic problems. Finally, the accuracy, convergence, and efficiency of the fast singular boundary method were validated through 2 numerical examples in comparison with analytical solutions, finite element solutions, and existing literature results. The effects of the Mach number and the wave number on acoustic propagation were also investigated.
- singular boundary method /
- fast algorithm /
- subsonic uniform flow /
- infinite domain /
- acoustic propagation
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注释:

1) 我刊青年编委傅卓佳来稿

HTML全文

图 1 源点的影响区域面积示意图

Figure 1. Illustration of the influence area of the source point

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图 2 流场中散射球模型

Figure 2. The scattering sphere model in the flow field

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图 3 ka=2，Ma=0.5时，RSF-SBM数值解与解析解的声压级对比

Figure 3. Comparison of sound pressure levels between RSF-SBM and analytical solutions for ka=2, Ma

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图 4 RSF-SBM与FMBEM^[8]的相对误差对比

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. Comparison of relative errors between RSF-SBM and FMBEM^[8]

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图 5 ka=20, Ma=0.2时，RSF-SBM和FMBEM^[8]的误差收敛曲线

Figure 5. Error convergence curves of RSF-SBM and FMBEM^[8] with ka=20, Ma=0.2

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图 6 飞机声散射模型

Figure 6. The acoustic scattering model for an airplane

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图 7 Ma=0，k=1时，RSF-SBM与COMSOL声压级结果对比

Figure 7. Comparison of sound pressure level results between RSF-SBM and COMSOL with Ma=0, k=1

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图 8 不同波数k下Ma=[0, 0.2, 0.4]时声压级极坐标图

Figure 8. Polar plots of sound pressure levels with different wave numbers k and Mach numbers Ma

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图 9 不同波数k及Mach数下飞机周围声压级分布云图

Figure 9. Sound pressure levels with different wave numbers k and Mach numbers Ma

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参考文献(30)

[1]	RIENSTRA S W, EVERSMAN W. A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts[J]. Journal of Fluid Mechanics, 2001, 437: 367-384. doi: 10.1017/S0022112001004438
[2]	WANG G, CUI X Y, FENG H, et al. A stable node-based smoothed finite element method for acoustic problems[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 297: 348-370. doi: 10.1016/j.cma.2015.09.005
[3]	ZARNEKOW M, IHLENBURG F, GRÄTSCH T. An efficient approach to the simulation of acoustic radiation from large structures with FEM[J]. Journal of Theoretical and Computational Acoustics, 2020, 28(4): 1950019. doi: 10.1142/S2591728519500191
[4]	CHENG A H D, CHENG D T. Heritage and early history of the boundary element method[J]. Engineering Analysis With Boundary Elements, 2005, 29(3): 268-302. doi: 10.1016/j.enganabound.2004.12.001
[5]	SHEN L, LIU Y J. An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation[J]. Computational Mechanics, 2007, 40: 461-472. doi: 10.1007/s00466-006-0121-2
[6]	ZHENG C J, BI C X, ZHANG C, et al. Fictitious eigenfrequencies in the BEM for interior acoustic problems[J]. Engineering Analysis With Boundary Elements, 2019, 104: 170-182. doi: 10.1016/j.enganabound.2019.03.042
[7]	LIU X, WU H, SUN R, et al. A fast multipole boundary element method for half-space acoustic problems in a subsonic uniform flow[J]. Engineering Analysis With Boundary Elements, 2022, 137: 16-28. doi: 10.1016/j.enganabound.2022.01.008
[8]	LIU X, WU H, JIANG W, et al. A fast multipole boundary element method for three-dimensional acoustic problems in a subsonic uniform flow[J]. International Journal for Numerical Methods in Fluids, 2021, 93(6): 1669-1689. doi: 10.1002/fld.4947
[9]	FAIRWEATHER G, KARAGEORGHIS A, MARTIN P A. The method of fundamental solutions for scattering and radiation problems[J]. Engineering Analysis With Boundary Elements, 2003, 27(7): 759-769. doi: 10.1016/S0955-7997(03)00017-1
[10]	BARNETT A H, BETCKE T. Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains[J]. Journal of Computational Physics, 2008, 227(14): 7003-7026. doi: 10.1016/j.jcp.2008.04.008
[11]	CHENG A H D, HONG Y. An overview of the method of fundamental solutions: solvability, uniqueness, convergence, and stability[J]. Engineering Analysis With Boundary Elements, 2020, 120: 118-152. doi: 10.1016/j.enganabound.2020.08.013
[12]	GU Y, CHEN W, HE X Q. Singular boundary method for steady-state heat conduction in three dimensional general anisotropic media[J]. International Journal of Heat and Mass Transfer, 2012, 55(17/18): 4837-4848. http://em.hhu.edu.cn/chenwen/papers/softmatter/201212.pdf?WebShieldDRSessionVerify=mDETPnNKhkwNkL8G1NCK
[13]	李煜冬, 王发杰, 陈文. 瞬态热传导的奇异边界法及其MATLAB实现[J]. 应用数学和力学, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225 LI Yudong, WANG Fajie, CHEN Wen. MATLAB implementation of a singular boundary method for transient heat conduction[J]. Applied Mathematics and Mechanics, 2019, 40(3): 259-268. (in Chinese) doi: 10.21656/1000-0887.390225
[14]	FU Z, XI Q, GU Y, et al. Singular boundary method: a review and computer implementation aspects[J]. Engineering Analysis With Boundary Elements, 2023, 147: 231-266. doi: 10.1016/j.enganabound.2022.12.004
[15]	GUMEROV N A, DURAISWAMI R. Fast Multipole Methods for the Helmholtz Equation in Tthree Dimensions[M]. Elsevier Science, 2005.
[16]	LIU Y. Fast Multipole Boundary Element Method: Theory and Applications in Engineering[M]. Cambridge: Cambridge University Press, 2009.
[17]	吴锋, 徐小明, 钟万勰. 广义特征值问题的快速傅里叶变换法[J]. 振动与冲击, 2014, 33(22): 67-71. WU Feng, XU Xiaoming, ZHONG Wanxie. Fast Fourier transform method for generalized eigenvalue problems[J]. Journal of Vibration and Shock, 2014, 33(22): 67-71. (in Chinese)
[18]	潘小敏, 盛新庆. 一种高性能并行多层快速多极子算法[J]. 电子学报, 2010, 38(3): 580-584. PAN Xiaomin, SHENG Xinqing. A high-performance parallel MLFMA[J]. Acta Electronica Sinica, 2010, 38(3): 580-584. (in Chinese)
[19]	吴海军, 蒋伟康, 刘轶军. 基于Burton-Miller边界积分方程的二维声学波动问题对角形式快速多极子边界元及其应用[J]. 应用数学和力学, 2011, 32(8): 920-933. doi: 10.3879/j.issn.1000-0887.2011.08.003 WU Haijun, JIANG Weikang, LIU Yijun. Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller BIE formulation and its applications[J]. Applied Mathematics and Mechanics, 2011, 32(8): 920-933. (in Chinese) doi: 10.3879/j.issn.1000-0887.2011.08.003
[20]	HO K L, GREENGARD L. A fast direct solver for structured linear systems by recursive skeletonization[J]. SIAM Journal on Scientific Computing, 2012, 34(5): A2507-A2532. doi: 10.1137/120866683
[21]	PAN X M, SHENG X Q. Preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm[J]. IEEE Transactions on Antennas and Propagation, 2013, 61(6): 3373-3377. doi: 10.1109/TAP.2013.2254450
[22]	MINDEN V, HO K L, DAMLE A, et al. A recursive skeletonization factorization based on strong admissibility[J]. Multiscale Modeling & Simulation, 2017, 15(2): 768-796. http://arxiv.org/pdf/1609.08130
[23]	HO K L, YING L. Hierarchical interpolative factorization for elliptic operators: integral equations[J]. Communications on Pure and Applied Mathematics, 2016, 69(7): 1314-1353. doi: 10.1002/cpa.21577
[24]	WU T W, LEE L. A direct boundary integral formulation for acoustic radiation in a subsonic uniform flow[J]. Journal of Sound and Vibration, 1994, 175(1): 51-63. doi: 10.1006/jsvi.1994.1310
[25]	CHEN W, GU Y. An improved formulation of singular boundary method[J]. Advances in Applied Mathematics and Mechanics, 2012, 4(5): 543-558. doi: 10.4208/aamm.10-m11118
[26]	SUN L L, CHEN W, CHENG A H D. Evaluating the origin intensity factor in the singular boundary method for three-dimensional dirichlet problems[J]. Advances in Applied Mathematics and Mechanics, 2017, 9(6): 1289-1311. doi: 10.4208/aamm.2015.m1153
[27]	LI J, FU Z, CHEN W, et al. A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation With high wavenumbers[J]. Engineering Analysis With Boundary Elements, 2019, 101: 165-172. doi: 10.1016/j.enganabound.2019.01.008
[28]	LIBERTY E, WOOLFE F, MARTINSSON P G, et al. Randomized algorithms for the low-rank approximation of matrices[J]. Proceedings of the National Academy of Sciences, 2007, 104(51): 20167-20172. doi: 10.1073/pnas.0709640104
[29]	WOOLFE F, LIBERTY E, ROKHLIN V, et al. A fast randomized algorithm for the approximation of matrices[J]. Applied and Computational Harmonic Analysis, 2008, 25(3): 335-366. doi: 10.1016/j.acha.2007.12.002
[30]	COMSOL. 飞机机身上的天线串扰仿真[EB/OL]. https://cn.comsol.com/model/simulating-antenna-crosstalk-on-an-airplanes-fuselage-18087.