[dchyrdvh]

I'm pretty sure that interference pattern from a sum of two waves is the sum of individual interference patterns. This should follow from how the wave equation looks.

The real physical solver doesn't do FFT, though. It makes the boundary circle vibrate with the input sound wave and effectively solves the wave equation where the boundary condition is u(0,t)=f(t) - the input sound.

I've run some calculations that solving the wave equation in real time would be infeasible. The convergence depends on the Courant number, which basically says that the grid step dx must be c*dt, i.e. the sound must travel on grid step per one time step. Since sound travels at 1.5 km/s in water, the grid needs to be super dense and 1 second of sound would need around 1 petaflops of calculations.