Invariance groups and reduction of the unsteady transonic small disturbance equation

Abstract

A geometric approach is undertaken towards the solution of the unsteady transonic small disturbance equation describing the low frequency flow field about a thin airfoil. From group properties given in Anderson and Ibragimov, Lie-Bäcklund Transformations in Applications (1979) we derive three invariance groups for the equation. Based on these groups a reduction of the equation is performed. The reduction leads to a steady equation and to an ordinary differential equation from which group invariant solutions of the unsteady transonic small disturbance equation can be obtained.