Implementation of an Acoustic 3D BEM with Visco-Thermal Losses

There is an increasing need in industry for numerical acoustic models including viscous and thermal losses of sound in air. Small devices such as couplers, microphones, mobile phones and hearing aids contain small cavities and passages where wave propagation cannot be assumed to be lossless. Viscous and thermal losses are relevant within the so-called viscous and thermal boundary layers, filling a significant part of the internal volume of these small devices. The fact that the loss mechanism is related to a boundary makes the Boundary Element Method a natural choice for this implementation.
In the present work, a three-dimensional BEM implementation based on the Kirchhoff decomposition of the Navier-Stokes equations into viscous, thermal and acoustic wave modes is described. The implementation details include: i) development of a vector velocity boundary condition and the coordinate changes involved, ii) tangential derivatives on the boundary using irregular meshes and iii) derivation of the acoustic variables in the domain.