Numerical Modeling of the Relaxation of a Body behind the Transmitted Shock Wave

Abstract: The problem about the interaction between a planar shock wave and cylinders of different mass is considered; the cylinders may move under the action of the pressure forces. This problem qualitatively corresponds to the problem about particle relaxation behind a shock wave. The mathematical model is based on the two-dimensional system of Euler equations. The computational algorithm is based on the Cartesian grid method for calculating the flows with the shock waves in the domains with varying geometry. The algorithm and its program realization are tested on the problem about the cylinder rising behind the shock wave. The curves of variation in the cylinder velocity are drawn, and the explanation on the qualitative form of the curves for a different cylinder mass is given. For a particular mass, the dynamics of the relaxation process are analyzed from the viewpoint of the transient shock-wave patterns realized in the interaction between the shock wave and the cylinder.