Report Number: CS-TR-67-70
Institution: Stanford University, Department of Computer Science
Title: On computation of flow patterns of compressible fluids in the transonic region
Author: Bergman, Stefan
Author: Herriot, John G.
Author: Richman, Paul L.
Date: July 1967
Abstract: The first task in devising a numerical procedure for solving a given problem is that of finding a constructive mathematical solution to the problem. But even after such a solution is found there is much to be done. Mathematical solutions normally involve infinite processes such as integration and differentiation as well as infinitely precise arithmetic and functions defined in arbitrarily involved ways. Numerical procedures suitable for a computer can involve only finite processes, fixed or at least bounded length arithmetic and rational functions. Thus one must find efficient methods which yield approximate solutions. Of interest here are the initial and boundary value problems for compressible fluid flow. Constructive solutions to these problems can be found in [Bergman, S., "On representation of stream functions of subsonic and supersonic flows of compressible fluids," Journal of Rational Mechanics and Analysis, v.4 (1955), no. 6, pp. 883-905]. As presented there, solution of the boundary value problem is limited to the subsonic region, and is given symbolically as a linear combination of orthogonal functions. A numerical continuation of this (subsonic) solution into the supersonic region can be done by using the (subsonic) solution and its derivative to set up an intial value problem. The solution to the initial value problem may then be valid in (some part of) the supersonic region. Whether this continuation will lead to a closed, meaningful flow is an open question. In this paper, we deal with the numerical solution of the initial value problem. We are currently working on the rest of the procedure described above.