Exact solution to the general Riemann problem in nonuniform and nonstationary media: A simplified analysis of a shock wave accelerated at a constant rate

Exact solutions to special cases of the general Riemann problem, in which two nonuniform and nonstationary flows are initially separated by a discontinuity at the origin, are proposed. By describing the evolution of flows using a family of the group-invariant solutions derived by Ovsiannikov [Dokl. Akad. Nauk S. S. S. R. 111, 439 (1958)] the flows ahead of and behind a shock wave accelerated at a constant rate are formulated analytically. Transition relations across a contact discontinuity and a characteristic wave in a nonuniform and nonstationary flow are formulated as well. The entire flow field is solved by combining these waves. (C) 2010 American Institute of Physics. [doi:10.1063/1.3527267]