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.
Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids
The present work aims at contributing to the investigation of methods to solve some classes of problems of acoustic propagation in thermo-viscous fluids, in unbounded or bounded media. The focus here is on thermal and vortical diffusion at the boundaries, which have to be considered for an accurate description of the acoustic field in small fluid-filled cavities and ducts. Existing boundary element or finite element acoustic software does not include these phenomena, as they are not compatible with the basic equations involved. A methodology is given to solve such problems when using this software, introducing a hybrid method which combines both numerical solutions and analytical solutions (for the fields inside the boundary layers). A detailed application is presented to validate the process using a boundary elements method.
An integral equation formulation for boundary element analysis of acoustic radiation problems in viscous fluids
Abstract This paper presents an integral equation formulation for acoustic radiation in viscous fluids, and its implementation to the numerical solution of two-dimensional problems. The thin acoustic boundary layer approximation has been made in determining fluid vorticity in the vicinity of solid boundaries. Numerical examples have been given to show the effect of viscosity on sound radiation. The paper also includes a discussion of the effect of viscosity on the non-uniqueness problem.