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The Preissmann box scheme and its modification for transcritical flows
Author(s) -
Freitag M. A.,
Morton K. W.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1908
Subject(s) - scheme (mathematics) , flow (mathematics) , simple (philosophy) , time stepping , open channel flow , computer science , channel (broadcasting) , mathematics , mechanics , calculus (dental) , mathematical analysis , physics , telecommunications , discretization , medicine , philosophy , dentistry , epistemology
The Preissmann box scheme is the standard numerical method used by hydraulic engineers to model open channel flows or surcharged flows in pipes; but it breaks down for transcritical flows. Various alternatives have been suggested for such cases, but we show how simple modifications of the difference scheme and its method of solution enable both to be used for such flows. Analysis of the double‐sweeping Thomas algorithm shows both how it works in the subcritical case and the effectiveness of its modification for transcritical flows. A well‐known analytical transcritical flow is used to demonstrate the accuracy of the new numerical scheme. Copyright © 2006 John Wiley & Sons, Ltd.