Some SEAC Computations of Subsonic Fluid Flows by Bergman’s Method of Integral Operators

Abstract

This chapter presents the results of some computations of two-dimensional irrotational subsonic compressible flow patterns which were carried out in the pseudo-logarithmic plane by means of Bergman’s method of integral operators. This is a method of superposition of particular solutions using integral operators to generate these solutions. A total of eleven particular solutions to the stream equation were obtained in the region .615 ⩽ M ⩽ .711, 0 ⩽ θ ⩽ .2. With these solutions at hand, and having computed by the same means certain fundamental singular solutions, a boundary value problem was set up in the pseudologarithmic plane which corresponds in the physical plane to a flow in a channel bounded by straight line segments and free boundaries. This boundary value problem was solved numerically by obtaining that linear combination of particular solutions which rendered the integral square error along the boundary a minimum. The computations were carried out on the National Bureau of Standards Eastern Automatic Computer (SEAC).