One-dimensional transport equation models for sound energy propagation in long spaces: theory

Inhomogeneous diffusion process in elongated rooms: An interpretation based on the dynamics of sound particles

Previous studies showed that the reverberant field in elongated rooms is governed by non-homogeneous diffusion. The objective of this study is to physically interpret this phenomenon by considering the dynamics of the sound particles. Starting from the original diffusion theory, a quantity that can be interpreted as a "local" mean free path has been proposed and computed from the paths of the propagating particles. Based on the proportionality relationship between the mean free path and the diffusion coefficient, the spatial distribution of the latter could be estimated and successfully compared with a direct estimation using the Fick's law.

Introduction to the Special Issue on Room Acoustic Modeling and Auralization

This Special Issue on Room Acoustic Modeling and Auralization contains nineteen research papers. A majority of the papers focus on various room acoustic simulation techniques, while the remaining ones concentrate on auralization of either simulation or measurement results. Using room acoustic simulation, the last paper in this issue presents a case study of the historic venue, Palais du Trocadero in Paris, France.

Investigation on the effect of aperture sizes and receiver positions in coupled rooms

Some recent concert hall designs have incorporated coupled reverberation chambers to the main hall that have stimulated a range of research activities in architectural acoustics. The coupling apertures between two or more coupled-volume systems are of central importance for sound propagation and sound energy decays throughout the coupled-volume systems. In addition, positions of sound sources and receivers relative to the aperture also have a profound influence on the sound energy distributions and decays. This work investigates the effect of aperture size on the behavior of coupled-volume systems using both acoustic scale-models and diffusion equation models. In these physical and numerical models, the sound source and receiver positions relative to the aperture are also investigated. Through systematic comparisons between results achieved from both physical scale models and numerical models, this work reveals valid ranges and limitations of the diffusion equation model for room-acoustic modeling.

A numerical investigation of the Fick's law of diffusion in room acoustics

In this paper the validity of the Fick's law of diffusion in room acoustics is investigated in the stationary state. The Fick's law, underlying the room-acoustics diffusion model, assumes a proportionality relationship between the local sound intensity and the energy density gradient, the proportionality constant being the so-called diffusion coefficient. This relationship, based on an analogy with the behavior of real particles in a scattering medium, is assessed by using a numerical tool simulating the actual dynamics of sound particles in a room. Two types of room geometries are considered: rooms with proportionate dimensions and long rooms. Concerning proportionate rooms the numerical analysis highlights the presence of weak variations of the reverberant energy density, generating an intensity vector pattern which is shown to be correctly described by the theoretical Fick's law and homogeneous diffusion. Conversely, inside long rooms, an estimate of the local value of the diffusion coefficient is carried out, showing that the reverberant sound field is well described by a spatially varying diffusion coefficient (non-homogeneous diffusion). The rate of increase of the estimated diffusion coefficient depends on the cross-sectional area of the room and on the boundaries absorption coefficient.

One-dimensional transport equation models for sound energy propagation in long spaces: simulations and experiments

In this paper, the accuracy and efficiency of the previously discussed one-dimensional transport equation models [Y. Jing et al., J. Acoust. Soc. Am. 127, 2312-2322 (2010)] are examined both numerically and experimentally. The finite element method is employed to solve the equations. Artificial diffusion is applied in the numerical implementation to suppress oscillations of the solution. The transport equation models are then compared with the ray-tracing based method for different scenarios. In general, they are in good agreement, and the transport equation models are substantially less time consuming. In addition, the two-group model is found to yield more accurate results than the one-group model for the tested cases. Lastly, acoustic experimental results obtained from a 1:10 long room scale-model are used to verify the transport equation models. The results suggest that the transport equation models are able to accurately model the sound field in a long space.