Time Domain Boundary Element Method for Room Acoustics
Hargreaves, J 2007, Time Domain Boundary Element Method for Room Acoustics, PhD, University of Salford, Salford, UK.
This thesis is about improving the suitability of the time domain Boundary Element Method (BEM) for predicting the scattering from surface treatments used to improve the acoustics of rooms. The discretised integral equations are typically solved by marching on in time from initial silence; however, this being iterative has potential for divergence. Such instability and high computational cost have prohibited the time domain BEM from widespread use. The underlying integral equation is known to not possess unique solutions at certain frequencies, physically interpreted as cavity resonances, and these manifest as resonant poles, all excited and potentially divergent due to numerical error. This has been addressed by others using the combined field integral equation; an approach built upon in this thesis. Accuracy and stability may also be compromised by poor discretisation and integration accuracy. The latter is investigated on real-world surfaces, demonstrating that the popular Gaussian integration schemes are not suitable in some circumstances. Instead a contour integration scheme capable of resolving the integrands‟ singular nature is developed. Schroeder diffusers are Room Acoustic treatments which comprise wells separated by thin fins. The algorithm is extended to model such surfaces, applying the combined field integral equation to the body and an open surface model to the fins. It is shown that this improves stability over an all open surface model. A new model for compliant surfaces is developed, comparable to the surface impedance model used in the frequency domain. This is implemented for surfaces with welled and absorbing sections, permitting modelling of a Schroeder diffuser as a box with surface impedances that simulate the delayed reflections caused by the wells. A Binary Amplitude Diffuser - a partially absorbing diffuser - is also modelled. These new models achieve good accuracy but not universal stability and avenues of future research are proposed to address the latter issue.
Final version of doctoral thesis with a few extra minor corrections marked in coloured text
Publisher / Institution
University of Salford