Pseudo-unsteady systems for steady inviscid flows

The first order partial differential equations of pseudo-unsteady type for the calculation of steady inviscid flows, compressible and isoenergetic, or incompressible, were studied. A family of such systems depending on five parameters is considered. The condition for a system to be hyperbolic with respect to time, and a condition relating to the number of eigenvalues of same given sign, are discussed as a function of these parameters. Examples of pseudo-unsteady systems are given, showing the very varied properties which these systems possess. There exist systems which are optimal with regard to an explicit numerical stability criterion. In flows which either are homentropic for a compressible fluid, or have uniform total pressure for an incompressible fluid, a two parameter family of simpler pseudo-unsteady systems is shown to exist.