Does anyone know of the solution to the bursting balloon problem? A balloon containing air at 2 bar in a 1 bar ambient, suddenly disintegrates. What is the pressure vs time and distance?

More broadly, we hope to understandneed the relation between explosion shock waves and launch vehicle sonic booms.

Are you talking about the Riemann problem?

I don't know the Riemann problem, can you describe it or give an online reference please.

(1). There is no relationship among the three: the bursting of a balloon, the explosion shock wave, and the sonic boom of a launch vehicle. (2). The first one is a rather weak shock with changing boundary. (3). The second one has a transient energy release. (4). The third one is supersonic flow over a blunt body. The far field of the curved shock becomes the sonic boom. (5). The last one is steady-state, while the first and the second are transient problems.

John, thanks for your helpful reply. I think the first two problems (balloon and explosion) have much in common: spherical symmetry, weakening shock waves. The third (launch vehicle which flies through thinning atmosphere, accelerates and turns) is hardly steady state.

All 3 cases need a propagating approach. In all cases the disturbance transitions from a strong shock near the source (with absorption), through a weak shock, then sound (without absorption) at greater distances.

In any case, do you know of a solution or an online reference?

Thanks Ian

I think a more well-known example is the collapse of a spherical bubble.

Yes, I think there is an analytical solution, I known there is a numerical one at least. Should be simple to do. take an inviscid bubble 1-D in spherical coordinates in a gravity free environment. assume all transport processes occur in the radial direction only.

Or if you just want a reference then check out publications by Matsumoto and therein...