An equivalent source method for acoustic problems with thermoviscous effects

Area of Science:

• Acoustics and Materials Science
• Computational Physics

Background:

• Sound propagation in small-scale acoustic structures is complex due to thermoviscous effects.
• Accurate modeling of these effects is crucial for designing micro-acoustic devices.

Purpose of the Study:

• To develop and validate an efficient equivalent source method (ESM) for analyzing sound propagation in small-scale acoustic structures with thermoviscous effects.
• To present coupled finite element method (FEM)-ESM formulations for acoustic-structural interaction.

Main Methods:

• Introduction of formulations for thermal, viscous, and acoustic modes in thermoviscous acoustics.
• Application of the equivalent source method (ESM) for efficient numerical computation.
• Coupling of ESM formulations at the boundary using isothermal, non-slip, and null-divergence conditions via two distinct strategies.
• Development of coupled finite element method (FEM)-ESM formulations for acoustic-structural interaction.

Main Results:

• The first ESM coupling strategy is efficient but requires evaluation of tangential velocity derivatives.
• The second ESM coupling strategy avoids tangential derivative evaluation but increases memory usage.
• Validated ESM formulations through benchmark examples.
• Demonstrated the coupled FEM-ESM formulation's validity via a simplified microphone analysis.

Conclusions:

• The equivalent source method (ESM) provides an efficient approach for analyzing sound propagation in small-scale acoustic structures with thermoviscous effects.
• The developed coupled FEM-ESM formulation is effective for acoustic-structural interaction problems.
• The study offers a robust numerical tool for micro-acoustic device design and analysis.