Numerical Simulation of Bed Load and Suspended Load Sediment Transport Using Well-Balanced Numerical Schemes

González-Aguirre, J.C.; Gonzalez-Vazquez, José A.; Alavez-Ramírez, Justino; Silva, R.; Vázquez-Cendón, M. Elena

doi:10.1007/s42967-021-00162-1

Cited by 5 publications

(5 citation statements)

References 33 publications

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“…Another test was conducted. The conserved variables are plotted at different times, specifically at t = 300, t = 600, and t = 900, and the results are shown in Figure ( 15). The results remain robust at different times, demonstrating the efficiency of the scheme.…”

Section: Comparison Between Pccu Methods and Hll Schemementioning

confidence: 89%

“…In some literature, sediment transport dynamics are modeled using a hydrodynamic sub-model based on shallow water equations coupled with the sediment concentration equation and the bedload equation, in the context of free-boundary nonhomogeneous water flow. Sediment transport in such situations has been studied numerically by [2], [6], [15], [19], [24], [23], [27], [44], [21], [33], [44] and experimentally in famous works as [12], [3], [32], [42]. Several sediment transport models have been previously developed.…”

Section: Introductionmentioning

confidence: 99%

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A new class of sediment transport models: Derivation and numerical solutions

Ndengna,

Bandji,

Njifenjou

2024

Preprint

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In coastal or estuarine environments the water fluctuations withgreater length of correlations are more intense and modify the meanmotion. The literature does not provide an averaged sedimenttransport model (STM) for coastal zones that accounts for both meanand fluctuating motions over an abrupt mobile bottom. Models basedon water are commonly used to describe sediment transport, but theyare not applicable when the flow becomes turbulent. These modelsonly consider the mean motion. To account the fluctuating motion ina STM, we assume $ |u -\overline{u}|^k \leq \tau^k h, \;\; k>0$ ($h= \mathcal{O}(\varepsilon)$ is the water depth, $\lambda = const$).However, distortion no exist always since during the dam break overerodible bed, the water near the bed can become dense thus weaklyturbulent. To always ensure the turbulence existence, we assume that$\tau = \mathcal{O}(\gamma^\alpha) \;\; \varepsilon^2 \ll \gamma \ll1$ and $\rho = \mathcal{O}(\gamma)$ with $\gamma = const$.Additionally we assume a weakly concentrated approximation ($d_{50}= \mathcal{O}(\varepsilon^\alpha)$, $\delta = \mathcal{O}(\epsilon),1< \alpha <3$) to derive the model. The model obtained in thisstudy builds upon previous work by authors in 2007, 2012, and 2018,while also improving upon more recent models developed in 2022 and2023. The hyperbolic STM is subject to various complexities arisingfrom turbulence and several nonlinear coupled terms. Furthermore,solving this problem still poses a computational challenge in termsof accuracy, convergence, robustness, and efficiency. To addressthis challenge, we propose a new path-conservative method called $\text{HLL}_{**}$, which we combine with a modified Averaging method.The Essentially Non-Oscillatory (AENO) nonlinear reconstructionmethod is used to approximate the model. This method is noteworthybecause it generalizes several HLL-based schemes developed in recentyears. Numerical test cases have been performed.

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Section: Comparison Between Pccu Methods and Hll Schemementioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

A new class of sediment transport models: Derivation and numerical solutions

Ndengna,

Bandji,

Njifenjou

2024

Preprint

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“…The riverbed evolution can be calculated from a sediment continuity equation, known as the Exner equation (Coleman & Nikora, 2009; González‐Aguirre et al, 2022):

((), 1 goodbreak- p^{'}) \frac{\partial Z_{b}}{\partial t} goodbreak+ \frac{\partial Q_{bs}}{\partial x} goodbreak+ \frac{\partial Q_{bn}}{\partial y} goodbreak= 0

where p' is a parameter depending on the porosity of the bed material (−) and Q bs and Q bn are bed‐load fluxes in the main‐flow direction ( s ) and cross‐flow direction ( n ), respectively (m 3 /ms). Z b is the bed evolution change (m).…”

Section: Methodsmentioning

confidence: 99%

“…The riverbed evolution can be calculated from a sediment continuity equation, known as the Exner equation (Coleman & Nikora, 2009;González-Aguirre et al, 2022):…”

Section: River Bed Shear Stress and River Bed Evolutionmentioning

confidence: 99%

Evaluating the physical habitat of riffle‐pool design in support of river habitat protection and rehabilitation

Wang,

Yang,

Bao

et al. 2023

Ecohydrology

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Riffle‐pool constructions are common practice in river management and fish conservation, but insufficient science exists to guide objective design of riffle‐pool. Understanding the spatial design of a riffle‐pool in river systems has significant value because it can provide important information to ameliorate aquatic species decline. In this study, six types of riffle‐pool structures were designed to assess hydrodynamic and riverbed morphology effects on stream habitat status. A two‐dimensional ecohydraulic model was used to assess the roles of different riffle‐pool designs in river habitat conditions. The natural flow condition and three types of flood flow conditions were applied to the six types of riffle‐pool structures to evaluate the habitat quality and the sustainability of the riffle‐pool design in mountain rivers. The long‐term impacts of the hydrodynamic and hydromorphology conditions on river physical habitat status were also analysed. The results indicate substantial differences in habitat quality among six riffle‐pool structures. It was found that narrow riffle‐pool construction yielded the best performance for the fish habitat, which had the best habitat quality among six riffle‐pool designs with the smallest pool area. In the same riffle‐pool structure, the habitat suitability in the riffle‐pool sequence will primarily increase more rapidly and then decrease gradually along with the discharge increase. Under the flood discharge scenarios, low flood discharge could improve riffle‐pool habitat quality, while high flood discharge could fragment the riffle‐pool habitat quality further. The long‐term hydrodynamic conditions have the same effects on all six cases. Overall, low discharge and smaller pool design would be beneficial to the river system, which could help maintain habitat diversity of mountain rivers. This analysis could provide valuable information for river management and decision‐making, which could assist in designing better mountain river habitats to promote conservation and rehabilitation of endangered biota.

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“…They conclude that both one-and two-dimensional numerical results are accurate and nicely capture small perturbations in the steady-state solution. Moreover, Gonzalez [44] used the finite volume scheme to solve the hyperbolic part of the governing system, computing the numerical flux in three ways: the Q-scheme of van Leer, the HLLCS approximate Riemann solution, with the final one considering the presence of non-conservative terms. The comparative study showed good agreement between experimental and numerical results.…”

Section: Introductionmentioning

confidence: 99%

A Comprehensive Numerical Overview of the Performance of Godunov Solutions Using Roe and Rusanov Schemes Applied to Dam-Break Flow

Elong,

Zhou,

Karney

et al. 2024

Water

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As open channel simulations are of great economic and human significance, many numerical approaches have been developed, with the Godunov schemes showing particular promise. To evaluate, confirm, and extend the simulation results of others, a variety of first- and second-order FVMs are available, with Rusanov and Roe schemes being used here to simulate the demanding case of 1D and 2D flows following a dam break. The virtual boundary cells approach is shown to achieve a monotonic solution for both interior and boundary cells, and while flux computation is employed at boundary cells, a refinement is only rarely used in existing models. A number of variations are explored, including the TVD MUSCL-Hancock (monotone upwind scheme for conservation laws) numerical scheme with several slope limiters in a quest to avoid spurious oscillations. The sensitivity of the results to both channel length and the ratio of downstream to initial upstream water depth is explored using 1D and 2D models. The Roe scheme with a Van Leer limiter as a slope limiter is shown to be both fast and slightly more accurate than other slope limiters for this problem, but the Rusanov scheme with different slope limiters works well for 1D simulations. Significantly, the selection of an appropriate slope limiter is shown to be best based on the ratio of the downstream to upstream water depth. However, this study focuses on the special case where the ratio of the initial depth downstream to upstream of the dam is equal to or less than 0.5, and these outcomes are compared to theoretical results. The 2D dam-break problem is used to further explore first- and second-order methods using different slope limiters, and the results show that the Superbee limiter can be problematic due to an observed large dispersion in depth contours. However, the most promising approaches from previous studies are confirmed to deserve the high regard given to them by many researchers.

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Numerical Simulation of Bed Load and Suspended Load Sediment Transport Using Well-Balanced Numerical Schemes

Cited by 5 publications

References 33 publications

A new class of sediment transport models: Derivation and numerical solutions

A new class of sediment transport models: Derivation and numerical solutions

Evaluating the physical habitat of riffle‐pool design in support of river habitat protection and rehabilitation

A Comprehensive Numerical Overview of the Performance of Godunov Solutions Using Roe and Rusanov Schemes Applied to Dam-Break Flow

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