On the modeling of narrow gaps using the standard boundary element method

Area of Science:

• Acoustics
• Computational Mechanics
• Numerical Analysis

Background:

• Standard numerical methods based on the Helmholtz integral equation are effective for low-frequency acoustic scattering and diffraction.
• These methods encounter degeneracy issues when applied to very thin objects or narrow gaps.
• Existing modified formulations often address thin-body problems but not narrow-gap scenarios.

Purpose of the Study:

• To investigate the degeneracy of standard axisymmetric Helmholtz integral equation formulations using the boundary element method (BEM).
• To present and test a simple integration technique to extend the applicability of the standard BEM formulation to thin objects and narrow gaps.
• To address limitations in modeling thin disks and narrow gaps in acoustic simulations.

Main Methods:

• Utilized a standard axisymmetric Helmholtz integral equation formulation.
• Employed a boundary element method (BEM) implementation.
• Tested a novel, simple integration technique on two cases: a thin rigid disk and two rigid cylinders with a variable gap.

Main Results:

• Confirmed degeneracy issues in the standard BEM for thin disks and narrow gaps.
• Demonstrated that the proposed simple integration technique effectively extends the range of tractable thicknesses and widths for the standard formulation.
• Validated the technique's applicability to both thin-body and narrow-gap acoustic problems.

Conclusions:

• The presented simple integration technique offers a practical solution to overcome BEM degeneracy for thin and narrow acoustic geometries.
• This method enhances the modeling capabilities for acoustic transducers and other applications involving complex geometries.
• The technique provides a valuable extension to standard numerical methods in acoustics.