Acoustic waves

Lattice Boltzmann Method LBM: Theory
#1

Hello,

I’d like to use LBM to model the propagation of acoustic waves in a microfluidic channel. In my case study, I have a kind of resonance chamber of about 2x2 mm and 500 um in height, and a bunch of piezoactuated tips that push against the bottom of the chamber. My question is, is a simple BGK scheme adapted to model this kind of effects? More specifically, what would be the Reynolds number in that case, and what would it depend on?

Thanks,

Greg

#2

Hey Greg,

I don’tknow if you passed throught the available books and thesis on this website, I’d give a look at this:

thesis

See you

Regards

#3

Hi,

It’s nice to see that my master’s thesis is getting at least a little interest. :slight_smile:

As a PhD student, I’m still looking at the LBM’s applicability for acoustics. I can tell you that at least for the BGK method, there are certain weaknesses:

  • Small errors in phase velocities and absorption coefficients
  • The bulk viscosity is fixed to 2/3 of the shear viscosity (this is actually roughly the same as air, where the ratio is 0.6)
  • The time step and spatial resolution cannot be very large since \tau cannot be arbitrarily close to 0.5 for accuracy and stability reasons. Still, you might be fine since you want to simulate a very small system.

You might want to take a look at this article: http://www.iet.ntnu.no/en/groups/akustikk/meetings/SSPA/2010/Viggen

I’m not quite sure what you mean by the Reynolds number, though. Reynolds numbers are used for the incompressible Navier-Stokes equation, whereas acoustics is a compressible phenomenon.

I hope that helps you!

Erlend M

#4

Cool! It seems ok for me though, as I want to simulate very small domains.

Thanks,

Greg