Modelling of acoustic viscothermal losses using the Boundary Element Method: From method to optimization

A range of acoustic engineering problems require the inclusion of viscous and thermal dissipation to be modelled accurately. The dissipative effects are especially relevant when the geometric dimensions of the acoustic domain become small which is the case in acoustic transducers and hearing aids. Computer-based numerical tools such as the Finite Element Method can be used to model and investigate the performance of acoustic devices without expensive prototyping.

Directly including acoustic dissipation into the Finite Element Method comes at a significant computational cost, sometimes making simulations on modest hardware problematic. An interesting alternative to the Finite Element Method, is the Boundary Element Method that is capable of including dissipation and at the same time avoid so-called boundary layer meshing.

However, a potential shortcoming of the existing boundary element implementation is its use of tangential derivative finite difference coupling terms, that may lead to undesirable inaccuracies. This work presents two new coupling strategies that avoid the use of finite difference by either using boundary element itself or the shape functions to estimate the tangential derivatives.

Numerical experiments demonstrate increased stability and error reduction when using the new coupling strategies. Furthermore, based on the improved viscothermal Boundary Element Method, a gradient-based shape optimization technique is developed. The shape optimization technique is used to optimize the absorption coefficient of two-dimensional quartewave and Helmholtz resonators located at an impedance tube termination.

Shape optimization results show that high absorption coefficients are only obtained when viscous and thermal dissipation is modelled accurately. The shape optimization technique has the future potential of improving the design of acoustic devices which require the inclusion of viscous and thermal dissipation.