Ill-posed design methods for the computation of inviscid flows

It is shown here that the solutions of the governing partial differential equations fail to behave well for three well-known methods of analysis and design for the computation of inviscid flows in turbomachines and for time-dependent transonic airflows. The first two examples are related to flows in turbomachines: the so-called 'streamline curvature methods' and the proposition of C. H. Wu to reduce the solution of an essentially three-dimensional internal flow problem to successive two-dimensional ones. Finally, time-dependent compressible and irrotational flows which employ the density and the velocity potential as dependent variables are considered.