Numerical simulation of discontinuous waves propagating over a dry bed. (Russian. English summary) Zbl 07811644
Zh. Vychisl. Mat. Mat. Fiz. 46, No. 7, 1322-1344 (2006); translation in Comput. Math. Math. Phys. 46, No. 7, 1254-1276 (2006).
Summary: 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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
numerical simulation; propagation of discontinuous waves; numerical methods in fluid dynamicsReferences:
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