Abstract
Finite-difference time-domain (FDTD) simulation has been a popular area of research in room acoustics due to its capability to simulate wave phenomena in a wide bandwidth directly in the time-domain. A downside of the method is that it introduces a direction and frequency dependent error to the simulated sound field due to the non-linear dispersion relation of the discrete system. In this study, the perceptual threshold of the dispersion error is measured in three-dimensional FDTD schemes as a function of simulation distance. Dispersion error is evaluated for three different explicit, non-staggered FDTD schemes using the numerical wavenumber in the direction of the worst-case error of each scheme. It is found that the thresholds for the different schemes do not vary significantly when the phase velocity error level is fixed. The thresholds are found to vary significantly between the different sound samples. The measured threshold for the audibility of dispersion error at the probability level of 82% correct discrimination for three-alternative forced choice is found to be 9.1 m of propagation in a free field, that leads to a maximum group delay error of 1.8 ms at 20 kHz with the chosen phase velocity error level of 2%.
Highlights
Simulation methods for the prediction of acoustic characteristics of rooms are common tools in the design process of critical listening rooms, performance spaces, and regular housing
The dispersion error of a finitedifference time-domain (FDTD) simulation has generally different characteristics in comparison to a narrow bandwidth group delay of an all-pass filter, the results indicate that the mean group delay error value (1.8 ms at 20 kHz) measured in this work is in line with the measured threshold values in existing studies
From the results of this study, we propose that a more meaningful approach in quantifying the dispersion error is to first specify the propagation distance of interest, and specify what group delay error is acceptable at that distance
Summary
Simulation methods for the prediction of acoustic characteristics of rooms are common tools in the design process of critical listening rooms, performance spaces, and regular housing. The finitedifference time-domain (FDTD) method has been studied for room acoustic prediction by several different authors. The parallel nature of the method makes it possible to efficiently use distributed computing in the time stepping, and allowing large domain sizes, which has made FDTD a viable option for wide bandwidth simulation. The dispersion error in FDTD schemes is such that the high frequency components travel with a different phase velocity than the low frequency components due to a non-linear phase response of the update operator. The dispersion error is dependent on the direction of the propagating wave. This leads to difficulties in a possible correction of the error in the simulated response because different propagation paths have different dispersion characteristics. A certain amount of dispersion error is inevitable in the simulated responses
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