Numerical Evaluation of Acoustic Green's Functions

The reduction of noise generated by new and existing engineering products is of increasing importance commercially, socially and environmentally. Commercially, the noise emission of vehicles, such as cars and aircraft, may often be considered a selling point and the effects of noise pollution on human health and the environment has led to legislation restricting the noise emissions of many engineering products. Noise prediction schemes are important tools to help us understand and develop a means of controlling noise. Acoustic problems present numerous challenges to traditional CFD-type numerical methods rendering all but the most trivial problems unsuitable. Difficulties relate to the length scale discrepancies which arise due to the relatively tiny pressure and density fluctuations of an acoustic wave propagating over large distancesto the point of interest; the result being large computational domains to capture wave behaviour accurately between source and observer. Noise prediction may be performed using a hybrid Computational Aero-Acoustics (CAA) scheme, an approach to noise prediction which alleviates many issues associated with exclusively numerical or analytical approaches. Hybrid schemes often rely on knowledge of a Green?s function, representing the scattering of the geometry, to propagate source fluctuations to the far-field. Presently, these functions only exist in analytical form for relatively simple geometries. This research develops principles for the robust calculation of Green?s functions for general situations. In order to achieve this, three techniques to computeGreen?s functions for the Helmholtz equation within an extended class of 2D geometries are developed, evaluated and compared. Where appropriate, their extension to 3D is described. Guidance is provided on the selection of a suitable numerical method in practice given knowledge of the geometry of interest. Through inclusion of the numerical methods for the construction of Green?s functions presented here, the applicability of existing hybrid schemes will be significantly extended. Thus, it is expected that noise predictions may be performed on a more general range of geometries while exploiting the computational efficiency of hybrid prediction schemes.