Numerical errors associated with the method of superposition for computing acoustic fields

The method of “wave superposition” is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources. The accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated. The ultimate objective of this study, then, is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and, consequently, the accuracy of the superposition solutions. In general, this is dependent upon the particular surface velocity distribution to be reconstructed, as well as other formulation factors such as the acoustic wave number, the number and locations of the surface nodes, and the number and locations of the point sources. Velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources. Numerical experiments on cylindrical radiators with different velocity distributions are performed to further illustrate how the solution accuracy depends on the surface velocity boundary condition as well as the other formulation factors.