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3 Archives of Hydro-Engineering and Environmental Mechanics

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A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

Prybytak D., Zima P.

Archives of Hydro-Engineering and Environmental Mechanics

2017

Vol. 64, nr 3-4

141--154

The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Artichowicz W., Prybytak D.

Archives of Hydro-Engineering and Environmental Mechanics

2015

Vol. 62, nr 3-4

101--119

In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow

Prybytak D.

Archives of Hydro-Engineering and Environmental Mechanics

2014

Vol. 61, nr 3-4

163–-173

The paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. This makes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a constant value of unknown functions was assumed. The verification was carried out for the case of flow in a square cavity with one moving wall. The results obtained show that the use of approximations by simple linear functions is relatively easy for different shapes of the area, but the result may be affected by significant errors.