There has been a lot of historical research carried out in transonic flows.
What constitutes a transonic flow? It is a mixed flow field with subsonic and supersonic regions.
In most cases of interest in aerodynamics, there is a wing immersed in a subsonic freestream with a local supersonic pocket on its surface. This mixed flow is characterized by a shock wave where the transition of Mach number from subsonic to supersonic occurs at Mach number 1. This mixed flow creates a challenging computational environment.
In addition, if we add the element of structural dynamics, the subsequent aeroelastic flowfield makes analysis nontrivial.