Similarity solutions for imploding strong shock waves in a van der Waals gas

In the present paper, the study presents a self-similar solution for the system of partial differential equations (PDEs) governing one-dimensional Euler equations modeled by a van der Waals equation of state. The method of Lie group of transformations is used to study the invariance and determine the class of self-similar solutions to the problem consisting of planar and symmetric flows of a van der Waals gas involving strong shocks. The ambient gas ahead of the shock is considered homogenous. One case of the collapse of an imploding shock is studied in detail for the radially symmetric flows. A software package "Mathematica" is used to perform all numerical calculations for determining the self-similarity exponent and also to draw the flow variables' profiles behind the shock. The effects of both parameters of van der Waals gas have also been shown.