The analytical solution of an unsteady gas flow with shocks

Abstract

A one-dimensional unsteady gas flow induced by an impulsive motion of a piston is studied by using a method of characteristics. The flow pattern in the nonisentropic flow region has been determined along particle paths emerging from the front shock into the region and along the positive characteristics emerging from the piston. The analytical solution obtained here enables us to determine the locations of the moving shock boundaries. It is found that the solution, which is also numerically computed and graphically presented, provides a good beginning toward the exact description of shock dynamics.