Numerical solution of the direct scattering problem through the transformed acoustical wave equation

Area of Science:

• Acoustics
• Computational Physics
• Wave Phenomena

Background:

• The acoustical wave equation traditionally involves pressure gradients, complicating numerical solutions.
• Accurate modeling of acoustic scattering is crucial for various applications, including sonar and medical imaging.

Purpose of the Study:

• To reformulate the acoustical wave equation to eliminate pressure gradients.
• To introduce a novel spectral method for solving the direct time-domain acoustic scattering problem.
• To present modeling techniques and numerical examples for validating the new approach.

Main Methods:

• A mathematical transformation was applied to the standard acoustical wave equation.
• A spectral method was developed for the numerical solution of the transformed equation.
• Numerical simulations were conducted to demonstrate the technique's efficacy.

Main Results:

• An equivalent form of the acoustical wave equation was derived, free from pressure gradients.
• The developed spectral method provides accurate solutions for time-domain scattering problems.
• Numerical examples confirm the effectiveness of the proposed modeling techniques.

Conclusions:

• The reformulated wave equation and spectral method offer a more efficient and accurate approach to acoustic scattering problems.
• This work advances numerical techniques in acoustics and wave modeling.
• The findings have potential implications for improving acoustic simulations in diverse fields.