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

Title:

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

Creator:

Artichowicz, Wojciech and Szymkiewicz, Romuald

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6f58ebf7-49e0-4f55-a300-31b402bd5739
uuid:6f58ebf7-49e0-4f55-a300-31b402bd5739
doi:10.2478/johh-2014-0031

Subject:

steady gradually varied flow, differential equations, and initial value problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

Slovak

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

226-233

Source:

Journal of hydrology and hydromechanics | 2014 Volume:62 | Number:3

Harvested from:

CDK

Metadata only:

false