Posted 2nd December 2020 by Holger Schmitz
Here is another animation that I made using the Vellamo fluid code. It shows two very simple simulations of spherical blast waves. The first simulation has been carried out in two dimensions. The second one shows a very similar setup but in three dimensions.
You might have seen some youtube videos on blast waves and dimensional analysis on the Sixty Symbols channel or on Numberphile. The criterion for the dimensional analysis given in those videos is true for strong blast waves. The simulation that I carried out, looks at the later stage of these waves when the energy peters out and the strong shock is replaced by a compression wave that travels at a constant velocity. You can still see some of the self-similar behaviour of the Sedov-Taylor solution during the very early stages of the explosion. But after the speed of the shock has slowed down to the sound speed, the compression wave continues to travel at the speed of sound, gradually losing its energy.
The video shows the energy density over time. The energy density includes the thermal energy as well as the kinetic energy of the gas.
For those of you who are interested in the maths and the physics, the code simulates the Euler equations of a compressible fluid. These equations are a model for an ideal adiabatic gas. For more information about the Euler equations check out my previous post.