Abstract
In the paper the mathematical model, describing the influence of snowmelt and rainfall run-off of given inflow and outflow of a part of a river system being studied in two-dimensional in space and nonstationary in time formulations, is presented. The Navier-Stokes equations for viscous incompressible liquid are taken as the starting point. Then, by height averaging, the shallow water equations serving as the basis for the mathematical model are obtained. Stable combinations of boundary and initial conditions for problems with controlled run-off of water are considered.
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References
Kuchment, L.S.: Models of Formation of River Run-off. Gidrometeoizdat, Leningrad (1980) (in Russian)
Vinogradov, Y.B.: Modeling of Formulation of Run-off. Gidrometeoizdat, Leningrad (1998) (in Russian)
Koren’, V.I.: Mathematical Models for Forecast of River Run-off. Gidrometeoizdat, Leningrad (1991) (in Russian)
Burakov, D.A.: Calculation of river floods with the use of analogues. Meteorology and hydrology 10, 79–88 (1982) (in Russian)
Burakov, D.A., Karepova, E.D., Shaidurov, V.V.: Mathematical modeling of run-off: theoretical basis, modern state, and outlook. Bulletin of Krasnoyarsk state university. Physics and Mathematics 4, 3–19 (2006) (in Russian)
Burakov, D.A., Avdeeva, Y.V.: Technology of on-line forecast of everyday water discharge (level) on the basis of satellite information on snow-covering (using Nizhnyaya Tunguska river as an example). Meteorology and hydrology 10, 75–87 (1996) (in Russian)
Burakov, D.A., Kashkin, V.B., Sukhinin, A.I., Romas’ko, V.Y., Ratnenko, I.V.: Methods for determining snow-covering of a eiver basin from satellite data for on-line run-off forecast. Meteorology and hydrology 8, 100–109 (1996) (in Russian)
Johnson, R.W. (ed.): The Handbook of Fluid Dynamics. CRC Press/ Springer, USA/Germany (1998)
Dronkers, I.: Calculation of Tides in Rivers and Coastal Water. Gidrometeoizdat, Leningrad (1967) (in Russian)
Rozhdestvenskii, B.L., Yanenko, N.I.: Systems of Quasilinear Equations and Their Applications in Gas Dynamics. Nauka, Moscow (1978) (in Russian)
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Burakov, D.A., Karepova, E.D., Shaidurov, V.V. (2011). Two-Dimensional Nonstationary Mathematical Model of Water Catchment. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_19
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DOI: https://doi.org/10.1007/978-3-642-17770-5_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17769-9
Online ISBN: 978-3-642-17770-5
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