On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

Fernández-Nieto, Enrique D.; Lucas, Carine; Luna, Tomás Morales de; Cordier, Stéphane

doi:10.1016/j.compfluid.2013.11.031

Cited by 16 publications

(21 citation statements)

References 31 publications

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“…A well‐known example of a sediment flux considering a threshold value is the Meyer‐Peter‐Müller formula

q_{s} false(t, x false) = A_{m} {((), τ^{⋆} - τ_{c}^{⋆})}_{+}^{3 false/ 2},

where A m is a constant parameter;

{false(\cdot false)}_{+} : = \max false(\cdot, 0 false)

τ_{c}^{⋆}

is a critical shear stress, basically equal to 0.047; τ ⋆ refers to a nondimensional friction term that is weighted by the buoyancy of the sediment particles

τ^{⋆} = \frac{ρ_{w} h T_{f}}{(ρ_{s} - ρ_{w}) d},

that is known as the Shields parameter, where ρ w , ρ s are the density of the water and the solid phase, respectively; and d is the mean granular diameter. Note that some authors recently introduced formulae that explicitly depend on the sediment depth b …”

Section: Description Of the Mathematical Modelmentioning

confidence: 99%

“…Note that some authors recently introduced formulae that explicitly depend on the sediment depth b. 34 Let us note that we will perform numerical test cases using the aforementioned formula, but the theoretical part of our paper works for a very general form of the friction coefficient and sediment flux as soon as they satisfy the general properties that will be precise hereafter.…”

Section: Closure Formulamentioning

confidence: 99%

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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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“…A well‐known example of a sediment flux considering a threshold value is the Meyer‐Peter‐Müller formula

q_{s} false(t, x false) = A_{m} {((), τ^{⋆} - τ_{c}^{⋆})}_{+}^{3 false/ 2},

where A m is a constant parameter;

{false(\cdot false)}_{+} : = \max false(\cdot, 0 false)

τ_{c}^{⋆}

is a critical shear stress, basically equal to 0.047; τ ⋆ refers to a nondimensional friction term that is weighted by the buoyancy of the sediment particles

τ^{⋆} = \frac{ρ_{w} h T_{f}}{(ρ_{s} - ρ_{w}) d},

Section: Description Of the Mathematical Modelmentioning

confidence: 99%

Section: Closure Formulamentioning

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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“…• Link with the effective and the critical Shields parameter. The stop criteria (23) gives us the way to find the relationship with the classical motion threshold. Thus, we introduce the modified shear stress including the gravitational forces, called the "effective shear stress", defined in our case as:…”

Section: Model Deduced With the Linear Friction Law (13)-(14)mentioning

confidence: 99%

Formal deduction of the Saint-Venant–Exner model including arbitrarily sloping sediment beds and associated energy

Fernández-Nieto¹,

Luna²,

Narbona-Reina³

et al. 2016

ESAIM: M2AN

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In this work we present a deduction of the Saint-Venant-Exner model through an asymptotic analysis of the Navier-Stokes equations. A multi-scale analysis is performed in order to take into account that the velocity of the sediment layer is smaller than the one of the fluid layer. This leads us to consider a shallow water type system for the fluid layer and a lubrication Reynolds equation for the sediment one. This deduction provides some improvements with respect to the classical SaintVenant-Exner model: (i) the deduced model has an associated energy. Moreover, it allows us to explain why classical models do not have an associated energy and how to modify them in order to recover a model with this property.(ii) The model incorporates naturally a necessary modification that must be taken into account in order to be applied to arbitrarily sloping beds. Furthermore, we show that this modification is different of the ones considered classically, and that it coincides with a classical one only if the solution has a constant free surface. (iii) The deduced solid transport discharge naturally depends on the thickness of the moving sediment layer, what allows to ensure sediment mass conservation. Moreover, we include a simplified version of the model for the case of quasi-stationary regimes. Some of these simplified models correspond to the generalization of classical ones such as MeyerPeter&Müller and Ashida-Michiue models. Three numerical tests are presented to study the evolution of a dune for several definition of the repose angle, to see the influence of the proposed definition of the effective shear stress in comparison with the classical one, and by comparing with experimental data.

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“…Undeniably, this has been triggered to a large extent by the growth in speed and memory capacity of electronic computers. Numerical simulations now enable us to tackle complex physical problems like never before [1]. Such problems involve the understanding and calculation of atmospheric behaviours.…”

Section: Introductionmentioning

confidence: 99%

Exploring the Interplay between CAD and FreeFem++ as an Energy Decision-Making Tool for Architectural Design

et al. 2018

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The energy modelling software tools commonly used for architectural purposes do not allow a straightforward real-time implementation within the architectural design programs. In addition, the surrounding exterior spaces of the building, including the inner courtyards, hardly present a specific treatment distinguishing these spaces from the general external temperature in the thermal simulations. This is a clear disadvantage when it comes to streamlining the design process in relation to the whole-building energy optimization. In this context, the present study aims to demonstrate the advantages of the FreeFem++ open source program for performing simulations in architectural environments. These simulations include microclimate tests that describe the interactions between a building architecture and its local exterior. The great potential of this mathematical tool can be realized through its complete system integration within CAD (Computer-Aided Design) software such as SketchUp or AutoCAD. In order to establish the suitability of FreeFem++ for the performance of simulations, the most widely employed energy simulation tools able to consider a proposed architectural geometry in a specific environment are compared. On the basis of this analysis, it can be concluded that FreeFem++ is the only program displaying the best features for the thermal performance simulation of these specific outdoor spaces, excluding the currently unavailable easy interaction with architectural drawing programs. The main contribution of this research is, in fact, the enhancement of FreeFem++ usability by proposing a simple intuitive method for the creation of building geometries and their respective meshing (pre-processing). FreeFem++ is also considered a tool for data analysis (post-processing) able to help engineers and architects with building energy-efficiency-related tasks.

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On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

Cited by 16 publications

References 31 publications

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

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

Formal deduction of the Saint-Venant–Exner model including arbitrarily sloping sediment beds and associated energy

Exploring the Interplay between CAD and FreeFem++ as an Energy Decision-Making Tool for Architectural Design

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