Exact analytic solutions describing unsteady plane gas flows with shocks of arbitrary strength

Several classes of exact analytic solutions for one-dimensional plane gas-dynamic equations describing piston-driven shocks propagating into inhomogeneous media are presented. These solutions are obtained by writing the conservation forms of the basic equations, and hence using their equivalent differential forms. These forms enable introduction of special coordinate systems which make it possible to exactly satisfy boundary conditions at the shock and at the piston. Previous results of Sachdev and Reddy [1] and Ustinov [2, 3] are recovered as special cases. Several representative solutions are shown graphically. Strong shocks as well as shocks of arbitrary strength and characteristic fronts are considered.