Computational issues of solving the 1D steady gradually varied flow equation
| Autor: | Wojciech Artichowicz, Romuald Szymkiewicz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Fluid Flow and Transfer Processes
Partial differential equation Differential equation Mechanical Engineering Weak solution Mathematical analysis First-order partial differential equation Exact differential equation differential equations TA Engineering (General). Civil engineering (General) Hydraulic engineering steady gradually varied flow Ordinary differential equation Riccati equation Initial value problem initial value problem TC1-978 Water Science and Technology Mathematics |
| Zdroj: | Journal of Hydrology and Hydromechanics, Vol 62, Iss 3, Pp 226-233 (2014) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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