How might one model the propagation of a sound wave through a 3D environment with obstacles in it?
My initial thought would be to use freely moving particles that repel one another; with sufficiently many particles I see no reason why the simulation wouldn't work.
However, if any particle could collide with any other then this introduces a huge complexity hit.
So I'm wondering whether the particles could be effectively anchored on a sphere packed lattice (dodecahedron?), so each particle has 18 neighbours. (you could think of placing one tennis ball on the table, then six fitting around it, now 6 can be fitted on top, and by symmetry 6 could be fitted underneath. so the original ball has 18 neighbours.
And then shockwaves could propagate through this mesh, and at each iteration each particle just needs to calculate the resultant force of its 18 neighbours acting on it.
I can't see whether this model would work or not. I suspect it is going to model sound propagating through a diamond rather than sound propagating through air, but isn't it going to be essentially the same?
Also, this isn't quite on topic for DSP, my apologies. Can anyone recommend a more suitable place to ask this question?