Validation of a Time-Domain Equivalent Source Method for Acoustic Scattering by an Oblate Spheroid

Abstract

*† ‡ The acoustic scattering of a plane wave by different oblate spheroids, including the limiting case of a circular disk, at arbitrary incidence angles is studied using the timedomain equivalent source method. The goal of the present work is to explore the capability of the equivalent source method for more complicated scattering surface shapes, particularly those surfaces with sharp edges. The oblate spheroid is chosen because an exact solution for the acoustic scattering exists. The predicted scattered acoustic pressure at arbitrary plane wave incident angles is compared to the exact solutions, which are determined numerically by calculating the oblate spheroidal radial and angle functions and their first derivatives. The agreement is excellent for a spherical shape. When the ratio of the semi-major axis ࢇ to semi-minor axis ࢈ is ࢇ/࢈ ൒ ૛ , the prediction starts to deviate from the exact solution, and when�ࢇ/࢈� ൐ ૡ.૙ , which means the oblate spheroid is approaching a disk, the result is significantly underpredicted. To attempt to determine the reason for this discrepancy, the sensitivity of the method to numerical parameters, such as the number of surface collocation points, the number and position of the equivalent sources, the time step, and the cut-off singular value, and the distribution of surface collocation points and equivalent sources, are investigated to provide guidance for parameter selection.