A quasianalytical time domain solution for scattering from a homogeneous sphere

Area of Science:

• Acoustics
• Computational Physics
• Numerical Analysis

Background:

• Acoustic scattering from objects is a fundamental problem in wave physics.
• Existing numerical methods often face challenges with mesh generation, singularities, or computational efficiency for transient problems.
• Time domain integral equation (TDIE) methods offer a promising alternative for analyzing transient wave phenomena.

Purpose of the Study:

• To develop a transient, mesh-free, and singularity-free solution for acoustic scattering from spherical objects.
• To apply this solution to sound-soft, sound-rigid, and penetrable scattering scenarios.
• To validate the accuracy and stability of the proposed method for broadband acoustic simulations.

Main Methods:

• A transient spherical multipole expansion-like solution within a TDIE framework.
• Expansion of the time domain Green's function for independent spatial and temporal convolution evaluation.
• Discretization of integral equations in space (using tesseral harmonics) and time, solved via the method of moments and a marching-on-in-time algorithm.
• Use of a band-limited temporal interpolant for efficient and accurate temporal convolution computation via numerical quadrature.

Main Results:

• The developed method provides accurate and stable solutions for acoustic scattering from spheres across different acoustic boundary conditions.
• Spatial integrals are evaluated in closed form using tesseral harmonics, enhancing computational efficiency.
• Accurate computation of temporal convolutions ensures late-time stability and precision of deconvolution data.
• Broadband simulation results demonstrate excellent accuracy and convergence when compared to analytical data.

Conclusions:

• The mesh-free and singularity-free TDIE framework offers a robust and efficient approach for transient acoustic scattering problems.
• The method's accuracy and stability are validated for various acoustic conditions and broadband simulations.
• This technique provides a valuable tool for analyzing complex acoustic wave-object interactions in the time domain.