Special Issue on Numerical Methods for Vibro–Acoustics and Aeroacoustics; Edited by S. Marburg and M. OchmannNo Access

Diffusion Equation-Based Finite Element Modeling of a Monumental Worship Space

Zühre Sü Gül

http://orcid.org/0000-0002-3655-9282

MEZZO Stüdyo Ltd, Turkey

E-mail Address: zuhre@mezzostudyo.com

Search for more papers by this author

Ning Xiang

Graduate Program in Architectural Acoustics, School of Architecture, Rensselaer Polytechnic Institute, USA

Search for more papers by this author

, and

Mehmet Çalışkan

Department of Mechanical Engineering, Middle East Technical University, Turkey

Search for more papers by this author

https://doi.org/10.1142/S0218396X17500291Cited by:3 (Source: Crossref)

Abstract

In this work, a diffusion equation model (DEM) is applied to a room acoustics case for in-depth sound field analysis. Background of the theory, the governing and boundary equations specifically applicable to this study are presented. A three-dimensional geometric model of a monumental worship space is composed. The DEM is solved over this model in a finite element framework to obtain sound energy densities. The sound field within the monument is numerically assessed; spatial sound energy distributions and flow vector analysis are conducted through the time-dependent DEM solutions.

Keywords:

References

1. W. C. Sabine, Collected Papers on Acoustics (Harvard University Press, Cambridge, 1922). Google Scholar
2. C. F. Eyring, Reverberation time in dead rooms, J. Acoust. Soc. Am. 168 (1930) 217–241. Crossref, Google Scholar
3. C. M. Harris, Application of wave theory of room acoustics to the design of auditoriums, Ann. Phys. 192(1) (1989) 59–65. Crossref, Web of Science, Google Scholar
4. D. Botteldooren, Finite-difference time-domain simulation of low-frequency room acoustic problems, J. Acoust. Soc. Am. 98 (1995) 3302–3308. Crossref, Web of Science, Google Scholar
5. M. Aretz and M. Vorländer, Efficient modelling of absorbing boundaries in room acoustic FE simulations, Acta Acust. United With Acust. 96 (2010) 1042–1050. Crossref, Web of Science, Google Scholar
6. L. Savioja and U. P. Svensson, Overview of geometrical room acoustics modeling techniques, J. Acoust. Soc. Am. 138 (2015) 708–730. Crossref, Web of Science, Google Scholar
7. J. H. Rindel, The use of computer modeling in room acoustics, J. Vibr. Eng. 3(4) (2000) 219–224. (Index 41–72 Paper of the International Conference BALTIC-ACOUSTIC 2000/ISSN 1392-8716). Google Scholar
8. E. N. Wester and B. R. Mace, A statistical analysis of acoustical energy flow in two coupled rectangular rooms, Acta Acust. 84 (1998) 114–121. Google Scholar
9. H. Kuttruff, Room Acoustics, 5th edn. (Spon Press, London, 2009). Google Scholar
10. J. Kang, Reverberation in rectangular long enclosures with diffusely reflecting boundaries, Acta Acust. United With Acust. 88 (2002) 77–87. Web of Science, Google Scholar
11. H. Zhang, Relaxation of sound fields in rooms of diffusely reflecting boundaries and its application in acoustical radiosity simulation, J. Acoust. Soc. Am. 119 (2006) 2189–2200. Crossref, Web of Science, Google Scholar
12. F. Ollendorff, Statistical room-acoustics as a problem of diffusion: A proposal, Acustica 21 (1969) 236–245. Google Scholar
13. V. Valeau, J. Picaut and M. Hodgson, On the use of a diffusion equation for room-acoustic prediction, J. Acoust. Soc. Am. 119(3) (2006) 1504–1513. Crossref, Web of Science, Google Scholar
14. A. Billon, V. Valeau, A. Sakout and J. Picaut, On the use of a diffusion model for acoustically coupled rooms, J. Acoust. Soc. Am. 120(4) (2006) 2043–2054. Crossref, Web of Science, Google Scholar
15. Y. Jing and N. Xiang, On boundary conditions for the diffusion equation in room acoustic prediction: Theory, simulations, and experiments, J. Acoust. Soc. Am. 123(1) (2008) 145–153. Crossref, Web of Science, Google Scholar
16. P. Luizard, J.-D. Polack and B. F. G. Katz, Sound energy decay in coupled spaces using a parametric analytical solution of a diffusion equation, J. Acoust. Soc. Am. 135 (2014) 2765–2776. Crossref, Web of Science, Google Scholar
17. Y. Jing, E. Larsen and N. Xiang, One-dimensional transport equation models for sound energy propagation in long spaces: Theory, J. Acoust. Soc. Am. 127 (2010) 2312–2322. Crossref, Web of Science, Google Scholar
18. Y. Jing and N. Xiang, One-dimensional transport equation models for sound energy propagation in long spaces: Simulations and experimental results, J. Acoust. Soc. Am. 127 (2010) 2323–2331. Crossref, Web of Science, Google Scholar
19. T. Polles, J. Picaut, M. Berengier and C. Bardos, Sound field modeling in a street canyon with partially diffusely reflecting boundaries by the transport theory, J. Acoust. Soc. Am 116 (2004) 2969–2983. Crossref, Web of Science, Google Scholar
20. J. M. Navarro, F. Jacobsen, J. Escolano and J. J. López, A theoretical approach to room acoustic simulations based on a radiative transfer model, Acta Acust. United With Acust. 96 (2010) 1078–1089. Crossref, Web of Science, Google Scholar
21. J. M. Navarro, J. Escolano and J. J. Lopez, Implementation and evaluation of a diffusion equation model based on finite difference schemes for sound field prediction in rooms, Appl. Acoust. 73 (2012) 659–665. Crossref, Web of Science, Google Scholar
22. N. Xiang, J. Escolano, J. M. Navarro and Y. Jing, Investigation on the effect of aperture sizes and receiver positions in coupled rooms, J. Acoust. Soc. Am. 133(6) (2013) 3975–3985. Crossref, Web of Science, Google Scholar
23. T. N. Narasimhan, The dichotomous history of diffusion, Phy. Today 62(7) (2009) 48–53. (2009 American Institute of Physics, S-0031-9228-0907-030-6/ISSN 0031-922). Google Scholar
24. R. Pierrat, J. J. Greffet and R. Carminati, Photon diffusion coefficient in scattering and absorbing media, J. Opt. Soc. Am. 23 (2006) 1106–1110. Crossref, Web of Science, Google Scholar
25. J. Picaut, L. Simon and J. D. Polack, A mathematical model of diffuse sound field based on a diffusion equation, Acta Acust. 83 (1997) 614–621. Google Scholar
26. Y. Jing and N. Xiang, A modified diffusion equation for room-acoustic predication (L), J. Acoust. Soc. Am. 121(6) (2007) 3284–3287. Crossref, Web of Science, Google Scholar
27. A. Billon, J. Picaut and A. Sakout, Prediction of the reverberation time in high absorbent room using a modified-diffusion model, Appl. Acoust. 69 (2008) 68–74. Crossref, Web of Science, Google Scholar
28. Y. Jing and N. Xiang, Visualizations of sound energy across coupled rooms using a diffusion equation model, Express Letter, J. Acoust. Soc. Am. 124(6) (2008) 360–365. Crossref, Web of Science, Google Scholar
29. N. Xiang, Y. Jing and A. C. Bockman, Investigation of acoustically coupled enclosures using a diffusion-equation model, J. Acoust. Soc. Am. 126(3) (2009) 1189–1198. Crossref, Web of Science, Google Scholar
30. J. Escolano, J. M. Navarro and J. J. López, On the limitation of a diffusion equation model for acoustic predictions of rooms with homogeneous dimensions, Letter to the Editor, J. Acoust. Soc. Am. 128(4) (2010) 1586–1589. Crossref, Web of Science, Google Scholar
31. C. Visentin, N. Prodi, V. Valeau and J. Picaut, A numerical investigation of the Fick’s law of diffusion in room acoustics, J. Acoust. Soc. Am. 132 (2012) 3180–3189. Crossref, Web of Science, Google Scholar
32. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953). Google Scholar
33. Z. Sü Gül, N. Xiang and M. Çalışkan, Investigations on sound energy decays and flows in a monumental mosque, J. Acoust. Soc. Am. 140(1) (2016) 344–355. Crossref, Web of Science, Google Scholar