Hello, relatively quick question, could go under physics, math, or computer science but I put it here.

 

I was just wondering if it is possible to create a Finite Difference Time Domain numerical simulation for sound waves similar to how it is possible to do it for electromagnetic waves.

 

Has anyone ever done this before? I've looked around but cant seem to find anything.

 

Does anyone know of any good sources to learn more about this if it has been done? Like papers, or books on acoustic design or something.

Simulation software exists for acoustics, and I have little doubt that some works in the time domain rather than frequency domain. The interrogation is rather: what does it bring, how fast and accurate is it?

 

I had considered such a software looong ago for wind music instruments. The design of such instruments takes advantage of software that tells for instance the embouchure impedance over many frequencies, and each frequency demands to solve a huge linear system. My hope was to emit just a pulse, let it propagate (hence no solving of an equation system) with all multiple echoes in the software's instrument model, collect the time response at the embouchure, and fourierize it to a frequency response.

 

Though, it has difficulties. For instance, it takes tiny time steps over a long interval to obtain a frequency response over many octaves. Worse, some processes are dispersive, especially the viscous and thermal losses which are all-important in music instruments, and these don't model naturally with a time-step algorithm - which translates to: complicated and slow.

 

The really bad news, at least for wind instruments, is that strong important losses result from turbulence. Predominant at a bassoon or a saxophone. A frequency-domain analysis doesn't model them properly, but a time-domain analysis could not run once for all frequencies. As well, wind instruments are sometimes nonlinear, as has been shown for the trombone playing ff, and then you can forget any Fourier transform.

 

For easier uses like room acoustics, noise damping and so on, it may be interesting.

Will comsol do it? Been quite a few years. I know it can do acoustic FEM, but something tells me it can do fdtd too.

 

It shouldn't be too different to implement than em, have you looked at meep?

 

A quick google provided this link http://www.k-wave.org/acousticsoftware.php

 

Yes they exist.