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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 3, Pages 401–417 (Mi vuu548)  

This article is cited in 1 scientific paper (total in 1 paper)

MECHANICS

The problem of boundary conditions for the shallow water equations

T. A. D'yakonova, S. S. Khrapov, A. V. Khoperskov

Volgograd State University, pr. Universitetskii, 100, Volgograd, 400062, Russia

Abstract: The problem of choice of boundary conditions is discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. While modeling unsteady surface water flows there is a dynamic boundary that partitions liquid and dry bottom. The situation is complicated by the emergence of sub- and supercritical flow regimes for the problems of seasonal floodplain flooding, flash floods, tsunami landfalls. Analysis of the use of various methods of setting conditions for the physical quantities of liquid at the settlement of the boundary shows the advantages of using the waterfall type conditions in the presence of strong heterogeneities of landforms. When there is a waterfall on the border of computational domain and heterogeneity of the relief in the vicinity of the boundary, a portion may occur which is formed by the region of critical flow with the formation of a hydraulic jump, which greatly weakens the effect of the waterfall on the flow pattern upstream.

Keywords: shallow water model, numerical schemes, boundary conditions, irregular bottom.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-07-01037
15-02-06204
15-45-02655-р_поволжье_а


DOI: https://doi.org/10.20537/vm160309

Full text: PDF file (676 kB)
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Bibliographic databases:

UDC: 519.6+532.5
MSC: 76D27
Received: 25.05.2016

Citation: T. A. D'yakonova, S. S. Khrapov, A. V. Khoperskov, “The problem of boundary conditions for the shallow water equations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:3 (2016), 401–417

Citation in format AMSBIB
\Bibitem{DyaKhrKho16}
\by T.~A.~D'yakonova, S.~S.~Khrapov, A.~V.~Khoperskov
\paper The problem of boundary conditions for the shallow water equations
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 3
\pages 401--417
\mathnet{http://mi.mathnet.ru/vuu548}
\crossref{https://doi.org/10.20537/vm160309}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3558450}
\elib{http://elibrary.ru/item.asp?id=26726586}


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    This publication is cited in the following articles:
    1. E. O. Agafonnikova, A. Yu. Klikunova, A. V. Khoperskov, “Computer simulation of the Volga river hydrological regime: problem of water-retaining dam optimal location”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:3 (2017), 148–155  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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