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A Godunov method for the computation of erosional shallow water transients. (English) Zbl 1028.76028

Summary: A Godunov method is proposed for the computation of open-channel flows under conditions of rapid bed erosion and intense sediment transport. Generalized shallow water equations govern the evolution of three distinct interfaces: the water free-surface, the boundary between pure water and a sediment transport layer, and the morphodynamic bottom profile. Based on the HLL scheme of Harten, Lax and van Leer [A. Harten, P. D. Lax and B. van Leer, SIAM Rev. 25, 35-61 (1983; Zbl 0565.65051)], a finite volume numerical solver is constructed, and then is extended to second-order accuracy using Strang splitting and MUSCL extrapolation. Lateralisation of the momentum flux is adopted to handle the non-conservative product associated with bottom slope. Computational results for erosional dam-break waves are compared with experimental measurements and semi-analytical Riemann solutions.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography

Citations:

Zbl 0565.65051

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