A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

Area of Science:

• Acoustics
• Computational Physics
• Wave Propagation

Background:

• The acoustic wave equation models wave propagation from physical laws, inherently generating scattering effects in heterogeneous media.
• Numerical simulations often require suppressing reflections to isolate transmitted wave fields for analysis and imaging.

Purpose of the Study:

• To develop a method for suppressing reflections in acoustic wave simulations.
• To modify constitutive relations to introduce direction-dependent wave attenuation.

Main Methods:

• A modification to constitutive relations was proposed, adding a term to suppress waves relative to a preferred direction.
• A staggered-grid, time-domain finite difference scheme was implemented.
• The acoustic Poynting-vector was used to determine local wave propagation direction.

Main Results:

• The method successfully suppressed reflections in media simulating bone tissue and geophysical structures.
• Only minor perturbations were observed in the transmitted wave field.
• A small increase in computation time was noted.

Conclusions:

• The modified acoustic wave theory effectively suppresses reflections while preserving the transmitted wave field.
• This approach is valuable for applications like medical ultrasound and geophysical exploration where transmitted wave analysis is crucial.