Instability of inviscid transonic flow in a channel

We study numerically inviscid transonic flow in a channel with a bump modelling an airfoil which is placed on the lower wall. The location of shock waves and supersonic zones are analysed for a range of the Mach number prescribed at the outlet. Computations demonstrate the existence of singular freestream Mach numbers which trigger off the flow instability and yield discontinuous changes in the steady flow structure and pressure distribution on the airfoil.