Meshing the Boundary Layer
When modeling using the Thermoviscous Acoustics interfaces, several length scales become important when setting up the mesh.
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First, there is the wavelength which should still be resolved as in pressure acoustics, see Meshing: Resolving the Waves in Space in the Pressure Acoustics Interfaces chapter. This length scale is often resolved as the geometries are small when modeling thermoviscous acoustic phenomena in microacoustic applications.
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Secondly, there is the thickness of the viscous and thermal boundary layers. In order for the model to include the correct amount of damping, the boundary layers need to be resolved. Ideally this is done using a Boundary Layers mesh. The Thickness of first boundary layer (or All layers) and the Number of boundary layers should be set such that they resolve the boundary layer at the specific modeling frequency or for the frequency range. Remember that the boundary layer thickness scales as one over the square root of the frequency.
The thermal and viscous boundary layer thickness length scale exists as a variable. In the frequency domain interface ta.d_visc and ta.d_therm that can be evaluated as function of frequency. In the transient interface tatd.d_visc and tatd.d_therm are evaluated at the frequency given by The maximum frequency to resolve setting in Transient Solver and Mesh Settings.
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Finally, it is important to consider the thickness of the boundary layer compared to the physical dimensions of the model, for example, the viscous boundary layer thickness δv compared to the tube radius a in a waveguide. This is sometimes known as the Womersley number
where δv is the viscous boundary layer thickness, δth is the thermal boundary layer thickness, and Pr is the Prandtl number.
When the boundary layer is small compared to the geometry, the Womersley number is large, say Wo > 10. Then the effect associated with the losses in the viscous boundary layer can normally be disregarded. In this case, the boundary layer do not need to be meshed and a Slip condition can be used instead of a No-slip condition. The same is true for the thermal boundary layer thickness compared to the tube radius. Here, an Isothermal condition can be replaced by an Adiabatic condition. If the No-slip or Isothermal conditions are still kept, then remember to add at least one boundary layer mesh that is of roughly the size of the acoustic boundary layer. If this is not done, erroneous losses can be introduced in the model.
On the other hand whenever Wo is O(1) or smaller, the boundary layer effects need to be included and the boundary layer needs to be meshed adequately as mentioned above.
A great deal of information about meshing and modeling with the Thermoviscous acoustics interface can be found in two COMSOL Blog posts. They are:
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 www.comsol.com/blogs/theory-thermoacoustics-acoustics-thermal-viscous-losses/
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 www.comsol.com/blogs/modeling-thermoacoustic-interface-comsol/
See the Boundary Layers section in the COMSOL Multiphysics Reference Manual for more details.