A method for computing acoustic fields based on the principle of wave superposition

TLDR

The superposition method is positioned as an alternative to boundary‑element methods, offering potential advantages in simplicity and computational efficiency. The study presents a method for computing acoustic fields of arbitrarily shaped radiators using the principle of wave superposition. The method employs a superposition integral equivalent to the Helmholtz integral, wherein an array of interior sources reproduces a prescribed surface velocity and the resulting source strengths are used to compute surface pressures. Numerical experiments demonstrate the method’s simplicity, with easier matrix element generation and improved accuracy and speed due to avoiding the uniqueness and singularity issues of boundary‑element formulations.

Abstract

A method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition. The superposition integral, which is shown to be equivalent to the Helmholtz integral, is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator. The strengths of the sources that produce this condition can, in turn, be used to compute the corresponding surface pressures. The results of several numerical experiments are presented that demonstrate the simplicity of the method. Also, the advantages that the superposition method has over the more commonly used boundary-element methods are discussed. These include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed, the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary-element formulation.