Invited Papers from the 12th International Conference on Theoretical and Computational Acoustics (ICTCA 2015); Guest Editor: Yuefeng SunNo Access

Comparison of Constant and Discontinuous Quadratic Boundary Elements for Exterior Axisymmetric Acoustic-Wave Propagation Problems

Sai Sudha Ramesh

Temasek Laboratories, National University of Singapore, 117576, Singapore

E-mail Address: tslssr@nus.edu.sg

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Kian-Meng Lim

Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore

E-mail Address: limkm@nus.edu.sg

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, and

Boo Cheong Khoo

Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore

E-mail Address: mpekbc@nus.edu.sg

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https://doi.org/10.1142/S0218396X15400032Cited by:6 (Source: Crossref)

Abstract

The present study involves numerical assessment of two types of boundary elements, namely constant and discontinuous quadratic elements based on a hypersingular Burton and Miller boundary integral formulation to tackle spurious frequencies manifesting in exterior problems. Convergence trends of the two types of boundary element with/without the inclusion of hypersingular formulation were studied for various combinations of boundary conditions and over a wide range of frequencies. The results indicate that discontinuous quadratic elements and constant elements give comparable results, with the quadratic elements being computationally more efficient as they take lesser computational time. Nevertheless, the constant element formulation is easier to implement, and it may be used for solving exterior wave propagation problems.

Keywords:

References

1. D. Givoli, Computational absorbing boundaries, in Computational Acoustics of Noise Propagation — Finite and Boundary Element Methods, eds. S. Marburg and B. Nolte (Springer-Verlag, Berlin, Germany, 2008), pp. 145–166. Crossref, Google Scholar
2. A. Bermudez, L. Hervella-Nieta, A. Prirto and R. Rodriguez, Perfectly matched layers, in Computational Acoustics of Noise Propagation — Finite and Boudnary Element Methods, eds. S. Marburg and B. Nolte (Springer-Verlag, Berlin, Germany, 2008), pp. 167–196. Crossref, Google Scholar
3. W. L. Meyer, W. A. Bell, B. T. Zinn and M. P. Stallybrass, Boundary integral solutions of three dimensional acoustic radiation problems, J. Sound Vib. 59 (1978) 245–262. Crossref, Web of Science, Google Scholar
4. F. Ursell, On the exterior problems of acoustics, Proc. Camb. Philos. Soc. 74 (1973) 117–125. Crossref, Web of Science, Google Scholar
5. T. Terai, On calculation of sound fields around three-dimensional objects by integral equations methods, J. Sound Vib. 69 (1980) 71–100. Crossref, Web of Science, Google Scholar
6. H. A. Schenck, Improved integral formulation of acoustic radiation problems, J. Acoust. Soc. Am. 44 (1968) 41–58. Crossref, Web of Science, Google Scholar
7. A. J. Burton and G. F. Miller, The application of the integral equation method to the numerical solution of some exterior boundary value problems, Proc. R. Soc. A 323 (1971) 201–210. Crossref, Google Scholar
8. A. F. Seybert, B. Soenarko, F. J. Rizzo and D. J. Shippy, A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions, J. Acoust. Soc. Am. 80 (1986) 1241–1247. Crossref, Web of Science, Google Scholar
9. B. Soenarko, A boundary element formulation for radiation of acoustic waves from axisymmetric bodies with arbitrary boundary conditions, J. Acoust. Soc. Am. 93 (1993) 631–639. Crossref, Web of Science, Google Scholar
10. A. H. W. M. Kuijpers, G. Verbeek and J. W. Verheij, An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration, J. Acoust. Soc. Am. 102 (1997) 1394–1401. Crossref, Web of Science, Google Scholar
11. W. L. Meyer, W. A. Bell, M. P. Stallybrass and B. T. Zinn, Prediction of the sound field radiated from axisymmetric surfaces, J. Acoust. Soc. Am. 65 (1979) 631–638. Crossref, Web of Science, Google Scholar
12. J. J. Grannell, J. J. Shirron and L. S. Couchman, A hierarchic $p$ $p$ -version boundary element method for axisymmetric acoustic scattering and radiation, J. Acoust. Soc. Am. 95 (1994) 2320–2329. Crossref, Web of Science, Google Scholar
13. W. Wang, N. Atalla and J. Nicolas, A boundary intergal approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions valid for all wave numbers, J. Acoust. Soc. Am. 101(3) (1997) 1468–1478. Crossref, Web of Science, Google Scholar
14. J. Zhao, G. R. Liu, H. Zheng, C. Cai and K. Y. Lam, A novel technique in boundary integral equations for analysing acoustic radiation from axisymmetric bodies, J. Sound Vibration 248(3) (2001) 461–475. Crossref, Web of Science, Google Scholar
15. A. K. Mohsen and M. Ochmann, Numerical experiments using CHIEF to treat the nonuniqueness in solving acoustic axisymmetric exterior problems via boundary integral equations, J. Advan. Res. 1(3) (2010) 227–232. Crossref, Google Scholar
16. S. Merz, S. Oberst, P. G. Dylejko, N. Kessissoglou, Y. K. Tso and S. Marburg, Development of coupled FE/BE models to investigate the structural and acoustic responses of a submerged vessel, J. Comput. Acoust. 15(1) (2007) 23–47. Link, Web of Science, Google Scholar
17. S. Merz, R. Kinns and N. Kessissoglou, Structural and acoustic responses of a submarine hull due to propeller forces, J. Sound Vib. 325 (2009) 266–286. Crossref, Web of Science, Google Scholar
18. H. Peters, N. Kessissoglou and S. Marburg, Modal decomposition of exterior acoustic-structure interaction, J. Acoust. Soc. Am. 133(5) (2013) 2668–2677. Crossref, Web of Science, Google Scholar
19. H. Peters, N. Kessissoglou and S. Marburg, Modal decomposition of exterior acoustic-structure interaction problems with model order reduction, J. Acoust. Soc. Am. 135(5) (2014) 2706–2717. Crossref, Web of Science, Google Scholar
20. H. Peters, R. Kinns and N. Kessissoglou, Effects of internal mass distribution and its isolation on the acoustic characteristics of a submerged hull, J. Sound Vib. 333(6) (2014) 1684–1697. Crossref, Web of Science, Google Scholar
21. S. S. Ramesh, K. M. Lim and B. C. Khoo, An axisymmetric hypersingular boundary integral formulation for simulating acoustic wave propagation in supercavitating flows, J. Sound Vib. 331(19) (2012) 4313–4342. Crossref, Web of Science, Google Scholar
22. S. S. Ramesh, K. M. Lim and B. C. Khoo, On the prediction of self-noise due to supercavitating underwater vehicle moving at subsonic speed using boundary element approach, in Proc. of ECUA 2012 11th European Conference on Underwater Acoustics, Edinburgh, Scotland, UK, Underwater Acoustics, Meetings on Acoustics, Vol. 17 (2013), pp. 1–9. Google Scholar
23. S. S. Ramesh, K. M. Lim, J. Zheng and B. C. Khoo, Numerical analysis of flow induced noise propagation in supercavitating vehicles at subsonic speeds, J. Acoust. Soc. Am. 135 (2014) 1752–1764. Crossref, Web of Science, Google Scholar
24. A. Becker, The Boundary Element Method in Engineering (Mc-Graw-Hill, UK, 1992). Google Scholar
25. V. Kupradze, Boundary Value Problems in Vibrational Theory and Integral Equations (Deutscher Verlag der Wissenschaften, Berlin, 1956). Google Scholar
26. H. Weyl and Kapazität von Strahlungsfeldern, Math. Z. 55 (1952) 187–198. Crossref, Google Scholar
27. T. W. Wu, The Helmholtz integral equation, Boundary Element Acoustics: Fundamentals and Computer Codes, Chap. 2 (WIT Press, Southampton, 2000), pp. 9–28. Google Scholar
28. J. T. Chen and H. K. Hong, Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series, Appl. Mech. Rev. 52(1) (1999) 17–33. Crossref, Google Scholar
29. C. C. Chien, H. Rajiyah and S. N. Atluri, An effective method for solving the hypersingular integral equations in 3-D acoustics, J. Acoust. Soc. Am. 88(2) (1990) 918–937. Crossref, Web of Science, Google Scholar
30. S. Marburg, The Burton and Miller method: Unlocking another mystery of its coupling, J. Comput. Acoust. 23 (2015), doi: 10.1142/S0218396X15500162. Google Scholar
31. G. Krishnasamy, F. J. Rizzo and T. J. Rudolphi, Continuity requirements for density functions in the boundary integral equation method, Comput. Mech. 9 (1992) 267–284. Crossref, Google Scholar
32. S. Marburg and S. Schneider, Influence of Element types on numerical error for acoustic boundry elements, J. Comput. Acoust. 11(3) (2003) 363–386. Link, Web of Science, Google Scholar
33. A. Tadeu and J. Antonio, Use of constant, linear and quadratic boundary elements in 3d wave diffraction analysis, Eng. Anal. Boundary Elements 24(2) (2000) 131–144. Crossref, Web of Science, Google Scholar
34. S. Marburg and S. Amini, Cat’s Eye radiation with boundary elements: Comparitive study on treatment of irregular frequencies, J. Comput. Acoust. 13(1) (2005) 21–45. Link, Web of Science, Google Scholar
35. E. A. Spence, S. N. Chandler-Wilde, I. G. Graham and V. P. Smyshlyaev, A new frequency-uniform coercive boundary integral equation for acoustic scattering. Comm. Pure Appl. Math. 64 (2011) 1384–1415. Crossref, Web of Science, Google Scholar
36. J. F. Zhuo, C. Wen, I. and G. Yan, A Burton–Miller-type singular boundary method for acoustic radiation and scattering. J. Sound Vib. 333 (2014) 3776–3793. Crossref, Web of Science, Google Scholar
37. M. S. Howe, A. M. Colgan and T. A. Brungart, On self-noise at the nose of a supercavitating vehicle, J. Sound Vib. 322(4) (2009) 772–784. Crossref, Web of Science, Google Scholar
38. M. S. Howe and A. W. Foley, Investigations of the sound generated by supercavity ventilation, D. I. T. C Report No. ME 09-13 (2009). Google Scholar