An assessment of the high frequency boundary element and Rayleigh integral approximations

This paper revisits the popular Rayleigh integral approximation and also considers a second approximation, the high frequency boundary element method, which is similar to the Rayleigh integral. The Rayleigh integral approximation under consideration is enhanced so that only the elements visible to a particular point in the field are used to calculate the sound pressure at that point. It is demonstrated how both the Rayleigh integral and high frequency boundary element method are approximations to the boundary integral equation so that similarities between the two methods are recognized. Several test cases were conducted in order to assess and compare both methods. The first set of test cases was the pulsating and oscillating sphere. Both methods were then compared on more applied examples including a running engine, construction cab, and transmission housing. It was concluded that though both methods can reliably predict the sound power for some problems, the high frequency boundary element method is the more robust.