Transonic flow

Summary

A transonic flow is a compressible flow that contains both subsonic and supersonic regions. This happens when the flight speed is close to the speed of sound. Consider a wing at a free stream Mach number of about $0.8$. A pocket of supersonic flow forms over its upper surface and usually ends in a shock wave. The steady equations of transonic flow are of mixed type, elliptic in the subsonic part and hyperbolic in the supersonic part, like the Tricomi equation. This makes transonic flow hard both in theory and in computation, and it governs the design of modern airliner wings.