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.
http://i.stanford.edu/pub/cstr/reports/cs/tr/67/70/CS-TR-67-70.pdf