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Abstract
In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximating the ordinary differential energy equation, which additionally coincides with the well-known standard step method usually applied for computing of the flow profile, can have variable number of roots. Consequently, more than one alternative solution corresponding to the same initial condition can be provided. Using this property it is possible to compute the water flow profile passing through the critical stage.
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- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.2478/johh-2014-0031
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Journal of Hydrology and Hydromechanics
no. 62,
edition 3,
pages 226 - 233,
ISSN: 0042-790X - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Artichowicz W., Szymkiewicz R.: Computational issues of solving the 1D steady gradually varied flow equation// Journal of Hydrology and Hydromechanics. -Vol. 62, iss. 3 (2014), s.226-233
- DOI:
- Digital Object Identifier (open in new tab) 10.2478/johh-2014-0031
- Verified by:
- Gdańsk University of Technology
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