https://doi.org/10.1140/epjp/s13360-022-03202-8
Regular Article
A multilayered shallow water model for sediment transport in flows over heterogeneous erodible beds
1
Department of Civil and Environmental Engineering, Imperial College London, South Kensington Campus, SW72AZ, London, UK
2
Department of Engineering, University of Durham, South Road, DH1 3LE, Durham, UK
Received:
28
April
2022
Accepted:
14
August
2022
Published online:
27
August
2022
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
