Nonlinear Green's function method for unsteady transonic flows

Abstract

Advantages to employing Green's function in describing unsteady three-dimensional transonic flows are explored. The development of the function for application to linear subsonic and supersonic unsteady aerodynamics is reviewed. It is shown that unique solutions are possible for external flows, with all functional expressions being defined in Prandtl-Glauert space. The development of methods of using the Green's function for transonic flows is traced, noting the necessity of including the effects of significant nonlinear terms. The steady-state problem is considered to demonstrate the shock-capturing ability of the method and the usefulness of the function in the incompressible, subsonic, transonic, and supersonic areas of potential unsteady three-dimensional flows around complex configurations. Computational time is asserted to be an order of magnitude less than with finite difference methods.