Transonic flow occurs around moving objects as they approach and cross the sound barrier. Serious problems can occur at this point such as shock waves and flow separation which can cause aircraft to spin out of control. A breakthrough in analysis of the solvability of boundary value problems have made it possible to investigate the development of efficient numerical methods for simulation of transonic flow over airfoil/wing at cruise conditions, leading to improved design (in supermanoeuvre aircraft for example), and the avoidance of these problems.