Acoustic scattering by two fluid confocal prolate spheroids

TL;DR

This paper develops an exact mathematical solution for the acoustic scattering problem involving two fluid confocal prolate spheroids, validated numerically, applicable across various media properties and frequencies.

Contribution

It introduces a novel spheroidal-function series solution for acoustic scattering by two fluid confocal prolate spheroids, with a comprehensive numerical implementation.

Findings

Solution is exact and validated independently.

Implementation handles arbitrary media properties and frequencies.

Provides a robust method for complex spheroidal scattering problems.

Abstract

The exact spheroidal-function series solution for the time-harmonic acoustic scattering of a plane wave by two fluid confocal prolate spheroids is developed and a numerical implementation is formulated and validated by independent methods. The two spheroids define three regions in which the acoustic fields are expanded in terms of spheroidal wave functions multiplied by unknown coefficients. These expansions are forced to satisfy the boundary conditions and by using the orthogonality properties of the involved functions an infinite matricial system for the coefficients is obtained. The resulting system is then solved through a truncation procedure. The implementation has no limitations regarding the sound speed and density of the three media involved or in the incidence frequency.