An Axisymmetrical Acoustic BEM Formulation Including Visco-Thermal Losses

Sound waves in air experience losses due to viscous friction and thermal exchange, which become particularly relevant in a thin boundary layer over the domain boundaries. The lossless wave equation can still be used when the thickness of the boundary layer is small as compared with the setup dimensions. However, this is not usually true for small devices such as microphones, hearing aids, couplers, MEMS devices, mobile phones, etc., and then the losses need to be modeled. In this paper a numerical implementation of the Boundary Element Method (BEM) which includes visco-thermal losses is presented. The formulation is based on the Kirchoff method, where acoustic, thermal and viscous effects are decoupled everywhere except at the boundaries. This BEM formulation does not impose geometrical restrictions to the setup and can be applied to any axisymmetrical object, as long as the division of the boundary into elements is adequate and the problem has a manageable size. The method can be extended to full three-dimensional BEM.