Failure of uniqueness in transonic flow (Q1195360)

(From the introduction.) It is well known that the solution of Euler's equations for rotational flow around a body is not uniquely determined when there are closed streamlines along which the circulation is unspecified. More surprising has been the discovery of profiles for which the potential flow is no longer unique in the transonic regime. Such examples furnish an excellent test of the reliability of codes in computational fluid dynamics. In this connection McGrattan's code has led us to the construction of airfoils for which the Euler solution of the transonic flow problem is not unique either, even though no closed streamlines are present. The purpose of this paper is to describe the profiles and to show how they were obtained.