Note on similarity transform and shock waves

Phase transitions of materials can be investigated by shock compression. It is necessary to obtain the equations governing the shock waves formation. We introduce the similarity variable $\xi =r/S\left(t\right)$ for the radial distance $r$ and the radius of the shock front $S\left(t\right)$ to handle the continuity equation ${\partial }_t\rho +{\partial }_r\left(\rho v\right)+2\rho v/r=0$ for the density $\rho (r,t)$ and for the radial velocity $v(r,t)$ considering a spherically symmetric flow. To illustrate our correct approach via a test case we make detailed as well as crucial remarks on Joy et al.’s (2021) paper.