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Boundary-value problems in the Fanno model for turbulent compressible flow

Published online by Cambridge University Press:  12 July 2007

S. P. Hastings ,
J. B. McLeod  and
W. C. Troy
S. P. Hastings
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
J. B. McLeod
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
W. C. Troy
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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Abstract

A recent paper of Ockendon et al. discusses the Fanno model for quasi-one-dimensional flow of gas in a tube, in situations where the flow is turbulent and the tube is long enough for wall drag to be important. Based on appropriate scalings and with associated boundary conditions they derive equations for similarity solutions and make predictions about travelling and evolving waves. In this paper the existence, uniqueness and asymptotic behaviour of these wave forms is proved rigorously. Techniques include shooting methods (both one- and two-parameter), appropriate changes of variables, and comparison techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 1 , February 2002 , pp. 121 - 140
Copyright
Copyright © Royal Society of Edinburgh 2002

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