Expansion solution for subsonic compressible flow

An expansion solution in the physical plane is developed for subsonic compressible fluid flow past an obstacle. Assuming that the stream is inviscid, isentropic, irrotational and steady, it is shown that the velocity potential may be expressed as a series of homogeneous Heun functions and radial distance terms. The basis of this analysis is Ludford's formal discussion of corresponding singularities in Bergman's Linear Integral Operator Method. A modification of these results permits reduction of the governing nonlinear partial differential equation to an ordinary, nonhomogeneous, linear differential equation. The expansion solution is compared with the Rayleigh-Janzen method and the Prandtl-Glauert theory. The comparison indicates that this expansion gives better results than other methods currently used. The simplicity and economy of this expansion solution facilitates direct practical application.