Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes

Benkhaldoun, Fayssal; Elmahi, I.; ̈d, Mohammed Seaı

doi:10.1016/j.jcp.2007.04.005

Cited by 101 publications

(61 citation statements)

References 34 publications

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“…The adaptive procedure used here is based on multilevel refinement and unrefinement, it is aimed at constructing an adaptive mesh which dynamically follows the unsteady solution of the physical problem. This procedure has been used in [17] for adaptive finite volume solution of a combustion system and in [6] for pollutant transport by shallow water flows. The algorithm begins by selecting some criterion (here based on the gradient of the sediment concentration), which permits to make the refinement and unrefinement decisions.…”

Section: Adaptivity Proceduresmentioning

confidence: 99%

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

Benkhaldoun

Elmahi

Sari

et al. 2013

Numerical Methods in Fluids

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(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.

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Section: Adaptivity Proceduresmentioning

confidence: 99%

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

Benkhaldoun

Elmahi

Sari

et al. 2013

Numerical Methods in Fluids

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“…Therefore the shock-capturing Godunov-type numerical schemes that have been widely applied to solve the shallow water equations can be directly adopted to resolve the integrated conservation laws (Toro, 2001). A number of models of this kind have been reported in literature in recent years and most of them focus on seeking stable and well-balanced numerical solutions in the context a shockcapturing Godunov-type scheme for applications related to wetting and drying over rough terrains (Murillo et al, 2005(Murillo et al, , 2006Benkhaldoun et al, 2007;Petti and Bosa, 2007;Murillo et al, 2008Murillo et al, , 2009Liang, 2010b;Murillo and García-Navarro, 2011;Cea and V azquez-Cend on, 2012). Among these, the well-balanced finite volume Godunov-type scheme presented recently by Liang (2010b) was incorporated with a non-negative reconstruction technique and so is more suitable for practical simulations that involve wetting and drying over complex domain topographies.…”

Section: Introductionmentioning

confidence: 99%

A robust coupled model for solute transport driven by severe flow conditions

Zhang

Liang

Wang

et al. 2015

Journal of Hydro-environment Research

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This paper introduces a computationally efficient model that solves a 4 Â 4 matrix form of the hyperbolic conservation laws consisting of the 2D shallow water and advection-diffusion equations. The model allows automatic shock-capturing due to the implementation of a finite volume Godunov-type scheme featured with an HLLC approximate Riemann solver. The numerical scheme is also able to provide well-balanced solutions and maintain non-negative water depth and solute concentration for applications involving wetting and drying over complex domain topographies. Implemented on a simplified adaptive grid system, the model can save 3e17 times of computational cost without compromising solution accuracy for those simulations with predominant localised complex hydrodynamic or flow features, as demonstrated by the numerical experiments. Therefore, the current model provides a potential tool for efficient simulation of large-scale solute transport as well as flow hydrodynamics during a highly transient flood event caused by dam failure or flash flooding.

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“…In this regard, it is noted that the extra data storage or computation may be highly costly as the array is huge. Benkhaldoun et al [18,24] employed the normalized pollution concentration or bed load transport rate as an adaptation indicator. In this method, if the normalized value exceeds the threshold, the cell is marked for refinement or coarsening.…”

Section: Non-uniform Rectangular Mesh and Adaptationmentioning

confidence: 99%

Coupled flood and sediment transport modelling with adaptive mesh refinement

Huang

Cao

Pender

et al. 2015

Sci. China Technol. Sci.

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Coupled flood and sediment transport modelling in large-scale domains has for long been hindered by the high computational cost. Adaptive mesh refinement is one of the viable ways to solving this problem without degrading the accuracy. This goal can be accomplished through mesh adaptation, e.g., mesh coarsening and refining based on the dynamic regime of the flow and sediment transport along with bed evolution. However, previous studies in this regard have been limited to cases either without involving sediment transport or featuring flow-sediment-bed decoupling and the assumption of sediment transport capacity, which are not generally justified. Here, a coupled hydrodynamic and non-capacity sediment transport model is developed on adaptive non-uniform rectangular mesh. The proposed model is validated against experimental tests and numerical results based on the fixed meshes. It is demonstrated that the proposed model can properly capture shock waves, resolve the wetting/drying transition and reproduce morphological evolution. Compared with models based on the fixed meshes, the proposed model features great advantage in computational efficiency and holds promise for wide applications.shallow water flow, sediment transport, adaptive mesh Citation:Huang W, Cao Z X, Pender G, et al. Coupled flood and sediment transport modelling with adaptive mesh refinement.

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Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes

Cited by 101 publications

References 34 publications

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

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

A robust coupled model for solute transport driven by severe flow conditions

Coupled flood and sediment transport modelling with adaptive mesh refinement

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