Rarefaction wave interaction for the unsteady transonic small disturbance equations

We study a Riemann problem for the unsteady transonic small disturbance equations that results in a diverging rarefaction problem. The self-similar reduction leads to a boundary value problem with equations that change type (hyperbolic-elliptic) and a sonic line that is a free boundary. We summarize the principal ideas and present the main features of the problem. The flow in the hyperbolic part can be described as a solution of a degenerate Goursat boundary problem, the interaction of the rarefaction wave with the subsonic region is illustrated and the subsonic flow is shown to satisfy a second order degenerate elliptic boundary problem with mixed boundary conditions. Key–Words: two-dimensional Riemann problem, rarefaction waves, unsteady transonic small disturbance equations, mixed-type equations, degenerate Goursat boundary problem, free boundary.