Padé approximants and their application to scattering from fluid media

Area of Science:

• Acoustics
• Computational Physics
• Fluid Dynamics

Background:

• Modeling acoustic wave propagation and scattering is crucial in various fields.
• Accurate simulation of sound speed contrast effects in heterogeneous media presents challenges.

Purpose of the Study:

• To develop and validate a numerical method for modeling acoustic pressure scattering from fluid occlusions.
• To enhance the applicability of asymptotic series expansions for significant sound speed contrasts.

Main Methods:

• Asymptotic series expansion of acoustic pressure.
• Application of Padé approximants to extend the range of sound speed contrast.
• Numerical implementation for scattering from circular cylinders and inhomogeneous media.

Main Results:

• Demonstrated improved convergence between exact and numerical solutions for cylindrical scattering.
• Presented a numerical solution for inhomogeneous media using reduced-order Padé approximants.
• Validated the effectiveness of the method for varying sound speed contrasts.

Conclusions:

• The proposed numerical method effectively models acoustic scattering from fluid occlusions.
• Padé approximants significantly extend the applicability of asymptotic methods for larger sound speed contrasts.
• The approach provides a robust tool for analyzing acoustic phenomena in complex media.