Room Acoustic Simulation Using Finite Difference Time Domain Method

Authors

Abstract

The growing use of industrial machinery, household appliances and etc, has increased undesirable noises. Thus, the need to control and reduce the undesirable noises in a closed space has caused a lot of interest in recent years. In this paper, the behavior of sound waves in a closed space is investigated using finite difference time domain method. For this reason, firstly, the wave equation is derived using the mass and momentum conservation equation and adiabatic state equation for an ideal compressible fluid. Then, the boundary condition equation for a closed space is obtained using the momentum conservation law and wall impedance equation. The obtained equations are discritized based on the finite difference time domain method. Finally, the wave equation is solved under the wall boundary condition with arbitrary absorption coefficient and impulse source initial condition. The results show the capability of the method for solving this kind of problems.

Keywords


 
 [1] Rindel  J.H., Naylor G. (1992)  Computer Modeling of Sound Fields in Rooms - The State of the Art and Outlook to the Future -. ICA 14, F2-1.
[2] Svensson U.P. (2002) Modelling Acoustic Spaces for Audio Virtual Reality. Work on Model based Proc. and Coding of Audio (MPCA), pages 109–116, Belgium.
[3] Krokstad A.,  Strom S. and Sorsdal S. (1968) Calculating the Acoustical Room Response by the Use of a Ray Tracing Method. J. of Sound and Vibration, 8(1):118125.
[4] Allen J., Berkley D. (1979) Image Method for Efficiently Simulating Small-Room Acoustics. J. Acoust. Soc. Am., 65(4):943950.
[5] Naylor G.M. (1993) ODEON Another Hybrid Room Acoustical Model. Appl. Acoust.,
 38:131–143.
[6] Yokota T. (2002) Visualization of Sound Propagation and Scattering in Rooms. Acoust. Sci. & Tech., 23, 1, p40-46.
[7] Kowalczyk K., van Walstijn M. (2008) Modelling Frequency Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations. J. Audio Eng. Soc., 56(7/8):569–583.
[8] Mitchell A.R., Wait R. (1977) The Finite Element Method in Partial Differential Equations. John Wiley & Sons, London.
[9] Kludszuweit. A. (1991) Time Iterative Boundary Element Method (TIBEM) ein neues numerisches verfahren der 4- dimensionalen systemanalyse von wellenvorgangen zur berechnung der raumimpulsantwort. Acustica, 75:17–27.
[10] de Cogan D. (1998) Transmission Line Matrix (TLM) Techniques for Diffusion Applications. Gordon and Breach Science Publishers, Amsterdam.
[11] Hofmann M. (2011)   Sound  Field Simulation  Using Finite Differences in the Time Domain (FDTD). Seminar on Selected Topics in Multimedia Communications , Universität Erlangen-Nürnberg.
[12] Botteldooren D. (1995)   Finite Difference Time Domain Simulation of Low Frequency Room Acoustic Problems. J. Acoust. Soc. Am., 98(6):3302–3308.
[13] Kuttruff H. (1973)   Room acoustics. Applied Science Publishers Ltd, London.
[14] Kowalczyk K. (2008)   Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces. Acta Acustica United With Acustica, Vol. 94, p891 –906.
[15] Crompton J.S., Gritter L.T., Yushanov S.Y., Koppenhoefer K.C and Magyari D. (2010)    Analysis of Acoustic Response of Rooms. COMSOL Conference  Boston.
[16] Egan M. D. (2007) Architectural Acoustics. J. Ross Publishing, Fort Lauderdale.
[17] Vercammen M. (2012) Sound Concentration Caused by Curved Surfaces, Eindhoven University press, Netherlands.