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 field's behaviour in rooms can be modelled using different theories, depending on the  approach applied for describing the sound wave propagation.

This thesis focuses on room acoustics modelling in enclosed spaces using energy diffusion processes. In this work,
how the diffusion equation theoretical model can simulate the sound field distribution in complex spaces is investigated.

The acoustic diffusion equation model has been actively studied in recent years, since it provides high efficiency and flexibility to the simulations of different 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 diffusion 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 diffusion equation model. In this work, the sound field is modelled by means of finite-difference schemes. The results of this study provide practical and simple solutions by showing a low  computational requirements in both time and memory consumption.

Finally, an evaluation of the acoustic diffusion equation model is carried out in order to study its performance for acoustic predictions in rooms. Special attention is paid to both temporal and spatial assumptions of the model.
In these simulations, different scenarios and configurations are used to compare predicted values with measurement results and predictions from other well-established geometrical acoustics methods.

In general, the results show that the acoustic diffusion equation model can be used to predict room-acoustics time criteria, such as reverberation time, with accuracy.  A deeper analysis reinforces the theoretical limitation that the diffusion equation is mainly valid for predicting the late part of the room impulse response.
Moreover, it is observed that the spatial dependence of the predicted parameters with the diffusion equation is partially modelled, presenting low variability between several receiver positions within the room, as expected according to the theoretical assumptions.