Geodesic
Numerical simulation of discontinuous waves propagating over a dry bed
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1322-1344 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical algorithm is proposed for simulating the propagation of discontinuous waves over a dry bed governed by the shallow water equations in the first approximation. The algorithm is based on a modified conservation law of total momentum that takes into account the concentrated momentum loss associated with the formation of local eddy structures within the framework of the long-wave approximation. The modified conservation law involves a heuristic parameter that is chosen so as to agree with laboratory experiments. Numerical results are presented for the formation, propagation, and transformation of a discontinuous wave arising in a complete or partial (in the planned case) collapse of a dam over a bed with a horizontal or sloping bottom or a bottom with a local obstacle in the tailwater area. 
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N. M. Borisova; V. V. Ostapenko. Numerical simulation of discontinuous waves propagating over a dry bed. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1322-1344. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a15/

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