An Iterative Physical Acoustics Method for Modeling Acoustic Scattering by Penetrable Objects

Efficient modeling of acoustic scattering from water-filled thin shells remains challenging due to prohibitive computational costs of rigorous methods and oversimplifications in ray-based approximations. This paper develops an iterative physical acoustics (IPA) method, presenting simple and explicit formulations for scattering by penetrable objects immersed in fluids. The method combines Kirchhoff integral frameworks with thin-plate effective boundary conditions, discretizes mid-surfaces into triangular facets, and iteratively converges pressure fields to characterize the mechanisms of multiple reflections and transmissions. Validated against analytical solutions, numerical simulations, and scaled experiments, IPA provides comprehensive field predictions encompassing internal cavity fields, external near-fields, and far-field scattering patterns within a unified framework. It achieves significant computational efficiency gains while maintaining engineering practicality, successfully reproducing distant-range highlights from these mechanisms in time-domain spectra. Limitations are observed at low frequencies and high-curvature regions where elastic wave effects become significant. The IPA framework enables engineering-efficient scattering analysis for complex thin-shell structures.