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Efficient computational models for shallow water flows over multilayer erodible beds

Thomas Rowan (Department of Engineering, University of Durham, Durham, UK)
Mohammed Seaid (Department of Engineering, University of Durham, Durham, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 23 August 2019

Issue publication date: 23 August 2019




The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems.


Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms.


This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions.


A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.



Rowan, T. and Seaid, M. (2019), "Efficient computational models for shallow water flows over multilayer erodible beds", Engineering Computations, Vol. 37 No. 2, pp. 401-429.



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