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A multilayered shallow water model for sediment transport in flows over heterogeneous erodible beds

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Abstract

A fast and accurate finite volume method for multilayered shallow water flows with mass exchange over erodible beds is developed. The governing equations consist of the multilayered shallow water equations for the hydraulic variables, a set of transport equations for the suspended sediments in each layer and a class of empirical equations for erosion and deposition effects. Mass exchange terms between layers are accounted for in both water flow and suspended sediments along with terms for sedimentary diffusion. The coupled models for each layer have been reformulated as a coupled system of conservation laws with source terms, and a two-step finite volume method is presented for its numerical solution. The method is simple, fast and second-order accurate. In the first step, the governing equations are rewritten in a non-conservative form and the numerical fluxes are calculated using the method of characteristics. In the second stage, the numerical solutions are updated in a conservative form using the finite volume discretization. Entrainment, deposition and diffusion rates are evaluated in the first stage of a splitting operator. Numerical results are presented for a multilayered dam-break problem over an erodible bed and also for a wind-driven recirculation problem over an erodible non-flat bed. The obtained results for these examples demonstrate the capabilities of the combined multilayered model and the finite volume method to accurately simulate shallow water flows with suspended sediments over erodible beds.Please confirm the corresponding author is correctly identified and amend if necessary.The corresponding author is correctly identified.

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Data Availability Statement

The data underlying the results can be obtained from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Imperial College London, South Kensington Campus, London, SW72AZ, UK

    Thomas Rowan

  2. Department of Engineering, University of Durham, South Road, Durham, DH1 3LE, UK

    Mohammed Seaid

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  1. Thomas Rowan
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  2. Mohammed Seaid
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Correspondence to Mohammed Seaid.

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Rowan, T., Seaid, M. A multilayered shallow water model for sediment transport in flows over heterogeneous erodible beds. Eur. Phys. J. Plus 137, 974 (2022). https://doi.org/10.1140/epjp/s13360-022-03202-8

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