Some exact solutions describing unsteady plane gas flows with shocks
Abstract
A new class of exact solutions of plane gasdynamic equations is found which describes pistondriven shocks into nonuniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into nonuniform media.
 Publication:

Quarterly of Applied Mathematics
 Pub Date:
 October 1982
 Bibcode:
 1982QApMa..40..249S
 Keywords:

 Computational Fluid Dynamics;
 Gas Dynamics;
 Shock Wave Propagation;
 Two Dimensional Flow;
 Unsteady Flow;
 Density Distribution;
 Flow Equations;
 One Dimensional Flow;
 Propagation Velocity;
 Similarity Theorem;
 Transformations (Mathematics);
 Fluid Mechanics and Heat Transfer