Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime

Audusse, Emmanuel; Boittin, Léa; Parisot, Martin

doi:10.1051/m2an/2021031

Cited by 3 publications

(3 citation statements)

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“…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%

“…The aim of this work is to propose a new mathematical model for sediment transport resulting from interactions between turbulent mixing flows. The article discusses the hydro-morphodynamics of the riverbed using a one-layer and one-phase approach, as illustrated in Figure ( 2)). The layer of clear water, suspended particles, and bedload are treated as a single layer.…”

Section: Introductionmentioning

confidence: 99%

“…The physical approach exposed in Fig. (2) leads to design a new bed-load equation that accounts the phase-lag effect and forces the hyperbolicity of the new global system of equations.…”

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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