Relaxation Techniques for Three-Dimensional Transonic Flow about Wings

Abstract

A relaxation procedure has been developed to treat the three-dimensional, transonic small-perturbation equations about finite lifting wings. A combination of two schemes is employed. For flow forward of the wing trailing edge the equations are written in terms of a velocity potential in order to minimize computer algebra and storage. For the remaining flowfield the equations are written in terms of the velocity components in order to simplify the enforcement of the Kutta condition. Difference equations and relaxation procedures are described for both schemes. The computational method automatically captures the embedded shock wave in the three-dimensional flowfield. Computed results agree with other inviscid methods and experiment.

A Finite-Difference Method for Transonic Airfoil Design

“…As demonstrated in Ref. 8 For the inverse calculation, u is specified at the body and values of w are computed by exactly the same procedure used for the two-dimensional solution (see Sec. III).…”

Nonlinear Green's Function Method for Unsteady Transonic Flows

“…(17) has the same capability. It should be emphasized that in order to yield accurate results it is necessary that the total 'amount of sources' in the field be conserved, -UI) (34) not be affected by the representation used for between X ± and X 2 .…”

Transonic flow potential method development at Ames research center

“…The Murman-Cole algorithm ''switches" the differencing type from central to upwind or vice versa as dictated by the local Mach number, maintaining stable operation for transonic flows-even those with strong shocks. At Ames, this idea was extended to axisymmetric bodies by Bailey [7] and Krupp and Murman [8], and to three-dimensional applications by Bailey and Steger [9] and Ballhaus and Bailey [10]. In all these applications, the nonconservative form of the TSD equation was used.…”