Shock wave kinematics in an inviscid gas with solid dust particles

In this article, a system of partial differential equations governing the one-dimensional motion of an inviscid gas with solid dust particles is considered. The evolutionary behavior of cylindrical and spherical shock waves in dusty gas is determined. For this, we used the method based on the kinematics of one-dimensional motion of shock waves to derive an infinite hierarchy of transport equations describing the strength of shock waves and induced discontinuity behind it. These equations are used to analyze the growth and decay behaviors of shock waves in a dusty gas. The first two truncation approximations are considered and the obtained results are compared with the results obtained by Guderley's exact solution and the characteristic rule.