The Numerical Calculation of Steady Inviscid Supercritical Flow Past Ellipsoids without Circulation

Abstract : The previous work of the author in which the subcritical flow past ellipsoids was calculated is extended to supercritical flows. The same ellipsoidal coordinate system is used, the body-surface boundary-condition is then applied exactly (in the numerical sense). By means of a transformation of one of the coordinates, the infinite flow field is brought into a finite space for the calculation. The complete continuity equation is approximated by the usual central differencing in the elliptic (subcritical) regions, whilst in the hyperbolic (supercritical) regions, the combination of central and non-central differencing as suggested by Albone and Jameson is used, in order to model the absence of upstream propagation of disturbances. Although shock waves appear in the calculations their shape and position is only approximately determined (as e.g. in transonic small perturbation theory) since the difference scheme only ensures continuity of the potential across the shock, the Rankine-Hugoniot equations not being satisfied. A number of results is presented, for flows aligned along the major and second axes, and also yawed relative to these two axes. (Author)