Pseudo-Unsteady Method for the Computation of Transonic Potential Flows

Abstract

A NEW pseudo-unsteady method has been developed for the computation of transonic two-dimensional steady inviscid flows. This method is based on a set of two equations, with artificial time derivative terms, derived from Euler's equations by assuming that the total enthalpy and entropy are constant throughout the flowfield, even during the transient state, so that only the steady-state solutions are of physical interest. This pseudo-unsteady system is hyperbolic; a stability criterion for explicit numerical schemes is determined from the knowledge of the characteristic cone. Discretization of this system is carried out directly in the physical plane for arbitrary curvilinear meshes by means of an extension of MacCormack's scheme. The domain of application is restricted to potential flows (but including weak shock waves). The main advantage of this method, by comparison with the widely used relaxation methods for the potential equation, is the simplicity of its implementation both in conservative form and for general flow configurations. Numerical applications have been carried out for transonic flows past cascades, in nozzles, and in channels.