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

Abstract

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...

Advances in building simulation and computational techniques: A review between 1987 and 2014

“…Among various geometry method category models, commonly used in engineering applications are Ray-tracing method [209], image source method [210] and hybrid method. Figure 5: Categories of different acoustic modeling approaches [204] Hybrid method can combine the advantages of different methods and improve accuracy of results.…”

“…A comprehensive summary of categories of different acoustic modeling approaches is presented in Figure 5 [204]. Wave-based method is capable of predicting the acoustics for the full frequency range of interest and solving sound propagation in inhomogeneous media in complex environments as in outdoor acoustics, thus attracting increased attentions in recent years [205].…”

Evaluation of the Diffusion Equation for Modeling Reverberant Electromagnetic Fields

“…The diffusion model can be derived from a radiative transport theory of "particles" (analogous to EM rays) in a cavity [12]. It assumes the existence of a diffuse EM field with average energy density [2], where denotes an average over a statistical ensemble of systems, for example, mode tuning configurations in an RC.…”

“…In (1) a single point source is assumed. The time independent Green's function for the diffusion equation in an unbounded space is given by [24] exp (12) This includes a spurious "direct" term, , close to the source, . It arises from the fact that near the source a diffuse field has not been established and the diffusion equation is therefore unable to correctly describe the physical inverse square law variation of the direct energy density.…”