Computational issues of solving the 1D steady gradually varied flow equation

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Title:Computational issues of solving the 1D steady gradually varied flow equation
Creators:
Artichowicz, Wojciech; wojartic at pg dot gda dot pl; Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland.
Szymkiewicz, Romuald; Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland.
Journal or Publication Title:
Journal of Hydrology and Hydromechanics, 62, 3, pp. 226-233
Uncontrolled Keywords:steady gradually varied flow, differential equations, initial value problem

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 wellknown 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.

Official URL: http://147.213.145.2/vc/vc1.asp

Title:Computational issues of solving the 1D steady gradually varied flow equation
Translated title:Computational issues of solving the 1D steady gradually varied flow equation
Creators:
Artichowicz, Wojciech; wojartic at pg dot gda dot pl; Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland.
Szymkiewicz, Romuald; Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland.
Uncontrolled Keywords:steady gradually varied flow, differential equations, initial value problem
Subjects:T Technology > TA Engineering (General). Civil engineering (General)
Divisions:Mathematics, Physics and Earth Sciences > Institute of Hydrodynamics > Journal of Hydrology and Hydromechanics
Journal or Publication Title:Journal of Hydrology and Hydromechanics
Volume:62
Number:3
Page Range:pp. 226-233
ISSN:0042-790X
Publisher:Institute of Hydrology of the Slovak Academy of Sciences and the Institute of Hydrodynamics of the Academy of Sciences of the Czech Republic
Related URLs:
URLURL Type
http://avi.lib.cas.cz/node/55Publisher
ID Code:8287
Item Type:Article
Deposited On:01 Oct 2014 13:27
Last Modified:01 Oct 2014 11:27

Citation

Artichowicz, Wojciech; Szymkiewicz, Romuald (2014) Computational issues of solving the 1D steady gradually varied flow equation. Journal of Hydrology and Hydromechanics, 62 (3). pp. 226-233. ISSN 0042-790X

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