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

LIAO Qiqi; XI Qiang; XU Wenzhi; FU Zhuojia

doi:10.21656/1000-0887.450339

Volume 46 Issue 6

Jun. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(6): 697-708

LIAO Qiqi, XI Qiang, XU Wenzhi, FU Zhuojia. A Fast Singular Boundary Method for Simulation of Infinite-Domain Acoustic Propagation in Subsonic Uniform Flow[J]. Applied Mathematics and Mechanics, 2025, 46(6): 697-708. doi: 10.21656/1000-0887.450339

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

doi: 10.21656/1000-0887.450339

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

Received Date: 2024-12-24
Rev Recd Date: 2025-03-30
Publish Date: 2025-06-01

Abstract

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

Contributed by FU Zhuojia, M.AMM Youth Editorial Board

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References(30)

References

[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.