An unstructured finite‐volume method for coupled models of suspended sediment and bed load transport in shallow‐water flows

Abstract

(2013) 'An unstructured nite-volume method for coupled models of suspended sediment and bed load transport in shallow-water ows.', International journal for numerical methods in uids., 72 (9). pp. 967-993. Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe aim of this work is to develop a well-balanced finite volume method for the accurate numerical solution of the equations governing suspended sediment and bed-load transport in twodimensional shallow water flows. The modelling system consists of three coupled model components: (i) the shallow water equations for the hydrodynamical model, (ii) a transport equation for the dispersion of suspended sediments, and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. In this paper, we also describe an adaptive procedure in the finite volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed-load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases which demonstrate the accuracy and robustness of the method and its applicability in predicting dam-break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon.

A finite volume shock‐capturing solver of the fully coupled shallow water‐sediment equations

“…This confirms the assumption made by Cao et al [1] that suspended sediment is the dominant transport mechanism. The results of CA3 are very similar to the results obtained by [25] who made the same assumptions used in CA3, although [25] proposed a different method of solving the bed morphological Equation (40e). It is clearly evident in Figures 14(d), 15 and 16 that most of the bed erosion occurs under the fast-moving bore front.…”

“…The bed is composed of uniform sediment, d D 4 mm, and is erodible along the entire channel length. The third case is similar to the model proposed by Benkhaldoun et al [25]. Three different variations of the test case were modelled, CA1, CA2 and CA3.…”

“…[11,24,25]) have solved Equation (1e) using finite volumes by including it in the eigenvalue problem. Some authors (e.g.…”

A subgrid based approach for morphodynamic modelling

“…First, the coarse grid discharge is interpolated linearly in streamwise direction (Equation 2). Second, the discharge is distributed over a sub-segment in the cross-flow direction based on the simplified momentum equation for steady, uniform flow (Equation 4). This provides a smooth velocity field that can result both in increase or decrease of the velocity if the depth increases.…”

“…However, this problem is still relevant today. There is an urgent need for accurate and efficient morphodynamic models, which can simulate the evolution of large areas over decades [4,5,6,7]. These models are needed to study the sustainability and management of river and coastal systems over long periods of time.…”