On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

Jing, Yun; Xiang, Ning

doi:10.1121/1.2805618

Cited by 52 publications

(59 citation statements)

References 17 publications

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“…The calculation of the effective absorption coefficient α e in rooms has been a long-time topic in room acoustics, and a variety of formulas have been given (Sabine, 1964;Eyring, 1930;Joyce, 1978Joyce, , 1980Hodgson, 1993;Beranek, 2006;Jing and Xiang, 2008). In this example, α e will be calculated based on the critical-distance results simulated from the hybrid modal expansion.…”

Section: Applications Effective Absorption Coefficientmentioning

confidence: 99%

A hybrid modal analysis for enclosed sound fields and its applications

Xu¹,

Sommerfeldt²,

Leishman³

2013

Proceedings of Meetings on Acoustics

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]. Since then, his interest in room acoustics has not diminished. More than six decades later, Maa proposed an idea of adding a monopole solution to the normal modal expansion to improve the accuracy in simulating the near-field sound field in rooms [D. Y. Maa, Acta Acust. (Beijing) 27, 385-388 (2002)]. Following this idea, a hybrid model that combines the free field Green's function and a modal expansion has been proposed by the authors based on a rigorous mathematical derivation [B. Xu et al, J. Acoust. Soc. Am.128, 2857Am.128, -2867Am.128, (2010]. The hybrid modal expansion can be further extended for complex sound sources by introducing the multipole expansion to the solution. In this paper, the theoretical derivation of the hybrid modal expansion will be reviewed, followed by examples demonstrating the use of the hybrid modal expansion in real-world applications.

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Section: Applications Effective Absorption Coefficientmentioning

confidence: 99%

A hybrid modal analysis for enclosed sound fields and its applications

Xu¹,

Sommerfeldt²,

Leishman³

2013

Proceedings of Meetings on Acoustics

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“…The diffusion model associated to the three boundary conditions introduced in (6), (7), and (8) is compared to experimental data both in terms of sound pressure level and in terms of reverberation time for a 8×8×1.2 m 3 flat room (for more details, see [34]). The three models agree well with the experimental data in terms of SPL, with a maximum deviation of about 2 dB (Figure 1).…”

Section: Application To a Flat Roommentioning

confidence: 99%

Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Billon

Picaut²,

Valeau

et al. 2012

Advances in Acoustics and Vibration

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Industrial spaces are known to be very noisy working environment. This noise exposure can be uncomfortable, tiring, or even harmful, at worst. Industrial spaces have several characteristics: they are often huge flat volumes fitted with many obstacles and sound sources. Moreover, they are usually surrounded by rooms where low noise levels are required. The existing prediction tools can seldom model all these phenomena accurately. In this paper, a prediction model based on a diffusion equation is presented. The successive developments carried out to deal with the various propagating phenomena met in industrial spaces are shown. For each phenomenon, numerical or experimental examples are given to highlight the validity of this model. It is also shown that its computation load is very little in comparison to ray-tracing-based methods. In addition, this model can be used as a reliable and flexible tool to study the physics of the coupling between rooms. Finally, an application to a virtual factory is presented.

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“…6.2.1, with an uniform absorption coecient that increases monotonically from 0.1 to 0.9 at all interior surfaces. The diusion equation model assumes that the overall absorption is not high [Valeau et al, 2006, Jing andXiang, 2008], and the range of absorption coecients has been chosen for illustrative purposes. The diusion equation model is implemented by FTCS scheme using the same conguration parameters as in Sec.…”

Section: Discussionmentioning

confidence: 99%

“…In previous works two kinds of boundary conditions have been presented, a homogeneous Neumann boundary condition ] where sound energy cannot escape from the room boundaries (its validity is discussed in [Jing and Xiang, 2008]); and a more realistic mixed boundary condition for general situations which allows energy exchanges with the boundaries ∂V .…”

Section: Boundary Conditionsmentioning

confidence: 99%

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Discrete-time modelling of diffusion processes for room acoustics simulation and analysis

Ruiz¹,

Miguel²

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Sound propagation in an enclosed space is a complex phenomenon that depends on the geometrical properties of the room and the absorption features of the boundary's surface materials. The sound eld's behaviour in rooms can be modelled using dierent theories, depending on the approach applied for describing the sound wave propagation.This thesis focuses on room acoustics modelling in enclosed spaces using energy diusion processes. In this work, how the diusion equation theoretical model can simulate the sound eld distribution in complex spaces is investigated.The acoustic diusion equation model has been actively studied in recent years, since it provides high eciency and exibility to the simulations of dierent types of enclosures; however, only a few research studies have been performed to deeply investigate the accuracy, advantages and limitations of this alternative method.A systematic derivation of the acoustic diusion equation method is developed, to establish the basis and assumptions of the model and to link it with the geometrical acoustics techniques. This also allows a proper description of its theoretical advantages and limitations.This thesis is also devoted to the numerical implementation issues concerning the acoustic diusion equation model. In this work, the sound eld is modelled by means of nite-dierence schemes. The results of this study provide practical and simple solutions by showing a low computational requirements in both time and memory consumption. ResumenLa propagación del sonido en una sala es un fenómeno complejo que depende de las propiedades geométricas del recinto y de las propiedades de absorción de los materiales que forman las supercies límite del mismo.El comportamiento del campo sonoro dentro de una sala puede modelarse mediante el uso de varias teorías dependiendo de la aproximación aplicada para describir la propagación de la onda de sonido.Esta tesis se centra en el modelado de la acústica de recintos cerrados usando procesos de difusión de la energía. En este trabajo, se investiga como el modelo teórico de la ecuación de difusión puede simular la distribución del campo sonoro.El modelo de la ecuación de difusión ha sido estudiado a lo largo de los últimos años de forma muy activa, dado que permite una alta exibilidad y eciencia en las simulaciones de diferentes tipos de salas; sin embargo, solo se han realizado unos pocos estudios de investigación sobre la precisión, ventajas y limitaciones de este método alternativo.Para poder establecer las bases y las suposiciones del modelo, así como para enlazarlo con las técnicas de la acústica geométrica, se ha desarrollado una derivación sistemática del método de la ecuación de difusión acústica. Esto permite también una adecuada descripción de sus ventajas y limitaciones teóricas.Esta tesis también esta dedicada a los detalles de implementación mediante métodos numéricos del modelo de la ecuación de difusión acústica. En este trabajo, el campo sonoro se ha modelado mediante esquemas de diferencias nitas. Los resultados de est...

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On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

Cited by 52 publications

References 17 publications

A hybrid modal analysis for enclosed sound fields and its applications

A hybrid modal analysis for enclosed sound fields and its applications

Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Discrete-time modelling of diffusion processes for room acoustics simulation and analysis

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