Relaxation approximation to bed-load sediment transport

Delis, A. I.; Papoglou, I.

doi:10.1016/j.cam.2007.02.003

Cited by 28 publications

(32 citation statements)

References 26 publications

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“…It is evident that the symmetry of the bed propagation is not deteriorated by the multiple mesh adaptations. Moreover, we remark that the computed results are in good agreement with alternative simulations using structured meshes [6,12]. Next, the results obtained for the test case with A = 1 are presented in Figure 10 for the quasisteady approach at three different times t = 50, 300, and 600 s corresponding to the time required by the sediment to reach the downstream boundary.…”

supporting

confidence: 64%

“…For purposes of verifying our finite volume scheme, we use a simplified test example of the evolution of an initially hump-shaped bed in a squared channel studied in [6,5,12] among others.…”

Section: Channel Flow On Moving Bedmentioning

confidence: 99%

“…On the other hand, numerical methods using discontinuous Galerkin techniques have been studied in [10,11] for a class of sediment transport problems. Numerical methods based on the relaxation approach have also been applied to sediment transport equations in [12]. However, most of these methods present results with an order of accuracy lower than that expected in the solutions for unstructured grids.…”

Section: Introductionmentioning

confidence: 96%

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A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

Benkhaldoun

Sahmim

Seaı̈d

2010

Numerical Methods in Fluids

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SUMMARYWe discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load 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 bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.

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supporting

confidence: 64%

Section: Channel Flow On Moving Bedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

Benkhaldoun

Sahmim

Seaı̈d

2010

Numerical Methods in Fluids

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“…These results demonstrate the ability of the adaptive SRNHS scheme to capture traveling discontinuities without generating nonphysical oscillations. In addition, the comparison with similar numerical results available in the literature [11,13,7] on the same test case is also satisfactory.…”

Section: One-dimensional Resultssupporting

confidence: 57%

Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix

Benkhaldoun¹,

Sahmim²,

Seaı̈d³

2009

SIAM J. Sci. Comput.

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We present a finite volume method for the numerical solution of the sediment transport equations in one and two space dimensions. The numerical fluxes are reconstructed using a modified Roe scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the sediment transport system. A well-balanced discretization is used for the treatment of source terms. The method is well balanced, nonoscillatory, and suitable for both structured and unstructured triangular meshes. An adaptive procedure is also considered for the two-dimensional problems to update the bed-load accounting for the interaction between the bed-load and the water flow. The proposed method is applied to several sediment transport problems in one and two space dimensions. The numerical results demonstrate high resolution of the proposed finite volume method and confirm its capability to provide accurate simulations for sediment transport problems under flow regimes with strong shocks.

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“…Comparative studies of both 1‐step and splitting approaches, sometimes called coupled and uncoupled approaches, have been performed in the last decade by several authors. () They mostly conclude to the bad behavior of the splitting approach and then give rise to several works where the authors investigate 1‐step approaches() by extending finite volume solvers developed in the early 2000's for the classical SW system to the SWExner system. We would like to emphasize that, in fact, they only conclude to the bad behavior of 1 possible way to perform the splitting approach, not of the splitting approach itself.…”

Section: Introductionmentioning

confidence: 99%

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Audusse

Chalons

Ung

2018

Numerical Methods in Fluids

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Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint-Venant-Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technic that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue two objectives. First we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. But, second, we reinterpret our scheme as a splitting technic and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.

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Relaxation approximation to bed-load sediment transport

Cited by 28 publications

References 26 publications

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

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