Model of steady river flow in the cross section of a curved channel

Potapov I.I., Potapov D.I.
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Modeling of channel processes in the study of coastal channel deformations requires the calculation of hydrodynamic flow parameters that take into account the existence of secondary transverse currents formed at channel curvature. Three-dimensional modeling of such processes is currently possible only for small model channels; for real river flows, reduced-dimensional models are needed. At the same time, the reduction of the problem from a three-dimensional model of the river flow movement to a two-dimensional flow model in the cross-section assumes that the hydrodynamic flow under consideration is quasi-stationary and the hypotheses about the asymptotic behavior of the flow along the flow coordinate of the cross-section are fulfilled for it. Taking into account these restrictions, a mathematical model of the problem of the a stationary turbulent calm river flow movement in a channel cross-section is formulated. The problem is formulated in a mixed formulation of velocity — “vortex – stream function”. As additional conditions for problem reducing, it is necessary to specify boundary conditions on the flow free surface for the velocity field, determined in the normal and tangential direction to the cross-section axis. It is assumed that the values of these velocities should be determined from the solution of auxiliary problems or obtained from field or experimental measurement data.

To solve the formulated problem, the finite element method in the Petrov – Galerkin formulation is used. Discrete analogue of the problem is obtained and an algorithm for solving it is proposed. Numerical studies have shown that, in general, the results obtained are in good agreement with known experimental data. The authors associate the obtained errors with the need to more accurately determine the circulation velocities field at crosssection of the flow by selecting and calibrating a more appropriate model for calculating turbulent viscosity and boundary conditions at the free boundary of the cross-section.

Keywords: river flow, open channel, riverbed bend, cross-section, finite element method
Citation in English: Potapov I.I., Potapov D.I. Model of steady river flow in the cross section of a curved channel // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1163-1178
Citation in English: Potapov I.I., Potapov D.I. Model of steady river flow in the cross section of a curved channel // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1163-1178
DOI: 10.20537/2076-7633-2024-16-5-1163-1178
URL: http://crm-en.ics.org.ru/journal/article/3523/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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