Sound field in long rooms with diffusely reflecting boundaries

Picaut, Judicaël; Simon, Laurent; Polack, Jean‐Dominique

doi:10.1016/s0003-682x(98)00032-2

Cited by 42 publications

(57 citation statements)

References 6 publications

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“…For one-dimension configurations, Picaut et al [19] obtained analytical solutions for the diffusion problem. Valeau et al [20] proposed a numerical implementation using the finite element method, permitting to simulate more realistic three-dimension configurations.…”

Section: Resolution Of the Diffusion Problemmentioning

confidence: 99%

“…Equation (20) describes the combination of two diffusion processes, one due to the walls and the other due to the scattering objects. The additional term in (19) takes into account the absorption of sound energy by the scattering objects. Figure 6 shows that the obtained agreement of the diffusion model with the experimental data [13] is very good, similar to the one obtained with a raytracing software [36].…”

Section: Diffusion By Scattering Objectsmentioning

confidence: 99%

“…By using a physical analogy with the diffusion of particles in a medium containing spherical scattering objects, as presented by Morse and Feshbach [18], they showed that the acoustic energy density may be the solution of a diffusion equation. This diffusion problem can be then analytically solved for one-dimensional configuration [19]. More recently, Valeau et al [20] have generalized this model to three-dimensional enclosures and proposed a numerical implementation of this model for room-acoustic predictions.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resolution Of the Diffusion Problemmentioning

confidence: 99%

Section: Diffusion By Scattering Objectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Billon

Picaut²,

Valeau

et al. 2012

Advances in Acoustics and Vibration

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“…Articles referred to the basis of the method (Picaut et al, 1997), concerned initially uncomplicated spaces (Picaut et al, 1999b), and even streets (Picaut et al, 1999a) with a low absorption coefficient. Then the model was equipped with the boundary conditions which allowed introducing different absorption coefficients .…”

Section: Introductionmentioning

confidence: 99%

Computing Reverberation Time in a 3D Room Model Using a Finite Difference Method Applied for the Diffusion Equation

Kraszewski¹

2012

Archives of Acoustics

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The article presents theoretical values of reverberation times calculated on the basis of the diffusion equation for three room models: flat, cubic, and long. The article shows that not only the average absorption coefficient, but also location of the absorbent material, as well as the place where the time is counted have an impact on the reverberation time, calculated on the basis of the diffusion equation. Despite that, the diffusion model is based on statistical assumptions. The primary goal of the article was to show that the model has geometrical features.

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“…This approach has been applied to several singlespace enclosure types including rectangular rooms , long rooms [Picaut et al, 1999b] and tted rooms [Valeau et al, 2007], as well as coupled-spaces [Valeau et al, 2004, Billon et al, 2006, Xiang et al, 2009.…”

Section: Motivation and Scope Of The Thesismentioning

confidence: 99%

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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Sound field in long rooms with diffusely reflecting boundaries

Cited by 42 publications

References 6 publications

Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Computing Reverberation Time in a 3D Room Model Using a Finite Difference Method Applied for the Diffusion Equation

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

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