Integration of the differential equations for plane compressible subsonic flows
Abstract
The method of integral operators is used to obtain a useful approximation of the stream function for the plane, steady, irrotational flow of a compressible inviscid fluid. After application of the Molenbroek transformation, the hodograph plane is distorted radially by the Chaplygin transformation, yielding a differential equation in the reduced stream function. Use is made of a correspondence principle, by which the solution for an incompressible fluid is used to obtain the solution for a compressible fluid. A simple approximation is found for the generating function in Gilbert's (1974) variant of the integral operator method, by which the approximation of the stress function is obtained.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 October 1976
 DOI:
 10.1002/zamm.19760561015
 Bibcode:
 1976ZaMM...56..450L
 Keywords:

 Compressible Flow;
 Flow Equations;
 Stream Functions (Fluids);
 Subsonic Flow;
 Two Dimensional Flow;
 Differential Equations;
 Inviscid Flow;
 Numerical Integration;
 Operators (Mathematics);
 Potential Flow;
 Fluid Mechanics and Heat Transfer