On inviscied isentropic flow models used for finite difference calculations of two-dimensional transonic flows with embedded shocks about airfoils

Properties of inviscid isentropic flow models underlying finite difference methods for the calculation of two-dimensional transonic flows with embedded shocks about airfoils are discussed and compared. Attention is drawn to the fact that the isentropic time-dependent model described by Magnus and Yoshihara and the isentropic model used in relaxation-type methods (e.g. Steger/Lomax, Garabedian/Korn, Jameson) are fundamentally different. It is pointed out that the two models each imply a different wave drag mechanism. From a comparison of the shock-jiomp relations of the different isentropic model with the Rankine-Hugoniot jump relations and a semi-quantitative ajialysis of wave drag, it is concluded that the model described by Magnus and Yoshihara provides the best approximation to non-isentropic Rankine-Hugeniot flow. In calculations of steady flow, however, the use of this model has no real advantage over using non-isentropic Rankine-Hugoniot flow as a model.