Geodesic
The problem of boundary conditions for the shallow water equations
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 401-417

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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. 
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     title = {The problem of boundary conditions for the shallow water equations},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a8/}
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T. A. D'yakonova; S. S. Khrapov; A. V. Khoperskov. The problem of boundary conditions for the shallow water equations. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 401-417. http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a8/