Piston driven shock waves in non-homogeneous planar media

In this work, we analyze in detail the problem of piston driven shock waves planar media. Similarity solutions to compressible hydrodynamics equations are developed, for a strong wave, generated by time dependent pressure piston, propagating non-homogeneous medium consisting an ideal gas. Power law temporal and spatial dependency is assumed initial density, respectively. The similarity written both Lagrangian Eulerian coordinates. It shown that take various qualitatively different forms according value density exponents. We show there exist families solutions, which propagates at constant speed, accelerates, or slows down. Similarly, types near either finite, vanishes, diverges. Finally, perform comprehensive comparison between hydrodynamic simulations, setting proper boundary conditions. A very good agreement reached, demonstrates usefulness analytic as code verification test problem.