A two step viscothermal acoustic FE method
Previously, the authors presented a finite element for viscothermal acoustics. This element has the velocity vector, the temperature and the pressure as degrees of freedom. It can be used, for example, to model sound propagation in miniature acoustical transducers. Unfortunately, the large number of coupled degrees of freedom can make the models big and time consuming to solve. A method with reduced calculation time has been developed. It is possible to partially decouple the temperature degree of freedom, as result of the differences in the characteristic length scales of acoustics and heat conduction. This leads to a method that uses two sequential steps. In the first step, a scalar field containing information about the thermal effects is calculated (not the temperature). This is a relatively small FE calculation. In the second step, the actual viscothermal acoustical equations are solved. This calculation uses the field calculated in the first step and has the velocity vector and the pressure as the degrees of freedom. The temperature is not a degree of freedom anymore, but it can be easily calculated in a post processing step. The required computational effort is reduced significantly, while the difference in the results, compared to the fully coupled method, is negligible. Along with the theoretical basis for the method, a specific FE calculation is presented to illustrate its accuracy and improvement in calculation time.
A finite element for viscothermal wave propagation
The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic 
boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain 
are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as 
hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that 
describes viscothermal wave propagation is needed to model such devices. 
For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can 
range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with 
negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately 
described by the low reduced frequency model. This model’s major drawback is that it is only defined for 
simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries. 
To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the 
LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to 
the LRF model, the viscothermal finite element can be used to analyze complicated geometries. 
This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in 
which the results of the finite element models are compared to measurements.
Prediction of the effects of entropy fluctuations on sound radiation from vibrating bodies using an integral equation approach
An integral equation, which is based on the free space Green function approach, is presented for the analysis of sound radiation from a vibrating surface into a viscous fluid by taking into account the small entropy fluctuations inherent in the process. The thin acoustic boundary layer approximation has been made in determining fluid vorticity and heat flux in the close vicinity of solid boundaries. Numerical examples have been given to show the visco-thermal effects on sound radiated from a vibrating surface and also the non-uniqueness problem.