Time-domain simulation of acoustic wave scattering and internal propagation from a gas bubble of various shapes

Abstract

Acoustic scattering and resonances of gas bubbles are computed using a time-domain simulation based on numerical solutions of the conservation laws. The time histories of scattered pressure and fluid velocity, outside and inside the bubble, are obtained simultaneously from an immersed-boundary method allowing for the investigation of exterior and interior fields for non-spherical geometries. The acoustic resonances of the bubble are investigated for various bubble sizes, shapes, and inner gas parameters and compared in limiting cases to the partial wave scattering solutions for spherical bubbles. The dynamics of the gas motion and its associated contribution to resonance response has received little attention in previous analytical and numerical formulations. In this study, the acoustic propagation and motion inside the interior gas is investigated with respect to the monopole resonance with the combined time-domain simulation and immersed-boundary method. For the non-spherical prolate and oblate shapes, the scattering and resonance behaviors are compared with the approximate analytical results based on the shape factor method. The simulation method can be extended to less-understood shapes relevant to underwater and physical acoustics, such as "pancake-shaped" or "cigar-shaped" bubbles, as well as to spatial and time-dependent forcing.