Characteristic Analysis of the Dynamics of Shock Wave Propagation in a Medium with a Nonuniform Density Distribution

This paper is devoted to the numerical study of shock wave (SW) propagation in a medium with a nonuniform density distribution. The mathematical model is based on the Euler equations, which are solved in the shock-attached frame. This approach makes it possible to carry out an accurate characteristic analysis of the problem. First, the problems of SW propagation in a medium with finite-length segments with linearly increasing and decreasing density are considered. The obtained results are compared with the known analytical solutions. Then the case of a continuous change in the density of the medium in front of the SW according to the sinusoidal law is considered. The resulting flow is described and explained using the results for the case of a linear density gradient.