The Structure of Rarefaction and Compression Flows in the Neighborhood of the Reflection Point of the “Boundary” Characteristic

In this paper, we analyze the structure of one-dimensional steady flows of an ideal (inviscid and non-heat-conducting) gas with plane and cylindrical waves in the neighborhood of the reflection point of the “boundary” $C^-$-characteristic. The latter characteristic separates the quiescent gas from the flow initiated by the motion of a piston that confines the gas. In the plane $rt$, where $r$ is the distance measured from the plane or the axis of symmetry and $t$ is time, the reflection point, which coincides with the point of intersection of the boundary characteristic with the $t$ axis, also coincides with the origin of coordinates. Under the gas expansion, the initial velocity of the piston may by finite. When the gas is compressed, the piston starts to move with zero initial velocity and finite acceleration whose absolute value does not exceed a certain known value. We extend the results of the analysis to steady flows that are realized under a uniform supersonic inflow into plane symmetric and axially symmetric nozzles and inlets.