Novosibirsk, Russia, May, 30 – June, 4, 2011

# International Conference "Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Numerical modeling of unsteady hydro-termical processes in water bodies

### Reporter: Воеводин А.Ф.

Fragment river basin involving hydro constructions cascade together with upstream and downstream reaches are considered.
Mathematical model has worked based of combined 0D, 1D and 2D models hydraulics open channels. The one-dimensional models have based of the hydrodynamics equations averaged on the cross-sections, the two-dimensional models have constructed on the basis of the same equations but averaged on the channel width [1, 2].
For upstream and downstream cross sections have assigned boundary conditions; in the flow junctions are given the conjunction conditions, which involving the balance relations and the conditions of a joining for a local resistance. The topological structure of a water bodies system is described of a graph. One- and two-dimensional regions with the distributing parameters are corresponded to branches of graph; upstream, downstream cross sections and so flow junctions are corresponded to tops of graph.
The numerical model is worked on the basis of absolute stable implicit difference schemes and special algorisms for the solutions of the systems of equations.
Calculate examples of the hydrodynamic parameters and temperature fields with the account of a heat exchange with environment and water density exchange at a temperature function [1, 2].

The research is fulfilled with support within the Program of RAS Presidium 16.7 and the grant RFBR № 09-01-98001-R-Sibirea-a.

[1]. Vasiliey O.F., Voevodin A.F., Nikiforovskaya V.S. Numerical modeling heat-stratified flows in systems of water bodies. // Vichislitelnie tehnologii, 2005, vol.10, №5, pp. 29-38,(in Russian).
[2]. Voevodin A.F., Nikiforovskaya V.S., Ovcharova A.S., Numerical methods for solving the problem on unsteady water motion at mouth reaches of rivers. In: Arctic and Antarctic Resources, 1983, vol. 378, “Gidrometeoizdat”, Russia, St.-Petersburg, pp. 23-34 (in Russian).

 Abstracts file: voevodin-nikiforov.doc Full text file: nikiforovskaia.pdf

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