A new model of roll waves: comparison with Brock’s experiments

Richard, Gaël Loïc; Gavrilyuk, Sergey

doi:10.1017/jfm.2012.96

Cited by 80 publications

(125 citation statements)

References 23 publications

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“…the model for shear shallow flow introduced in [22] and extended in 2D in [11] and the bilayer version of the layerwise model for hydrostatic flows introduced in [4]. Let us begin by considering this latter model [4] which is a layerwise discretized Euler system.…”

Section: Relations With Other Shallow Water Type Modelsmentioning

confidence: 99%

“…Let us now consider the model introduced in [22], or, more precisely, its two dimensional extension presented in [11]. It reads…”

Section: Relations With Other Shallow Water Type Modelsmentioning

confidence: 99%

“…But Model (1) is also, as such, an improvement in the modeling of free surface shallow flows since it involves a new degree of freedom that takes into account the vertical shear in the flow. Similar models have been recently proposed to analyze particular regimes such as roll waves or hydraulic jumps in 1D [22,24] and in 2D [11], see also [6] for an extension to non hydrostatic flows. Up to our knowledge, it is the first time that the Riemann problem is analyzed in details for a shallow water model with two velocities.…”

Section: Introductionmentioning

confidence: 97%

“…In section 1, we first detail similarities between Model (1) and other models mentioned in the Introduction, in particular [4,11,22]. Then we exhibit its main properties.…”

Section: Introductionmentioning

confidence: 97%

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Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

Aguillon¹,

Audusse²,

Godlewski³

et al. 2018

SIAM J. Math. Anal.

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Some shallow water type models describing the vertical profile of the horizontal velocity with several degrees of freedom have been recently proposed. The question addressed in the current work is the hyperbolicity of a shallow water model with two velocities. The model is written in a nonconservative form and the analysis of its eigenstructure shows the possibility that two eigenvalues coincide. A definition of the nonconservative product is given which enables us to analyse the resonance and coalescence of waves. Eventually, we prove the well-posedness of the two dimensional Riemann problem with initial condition constant by half-plane.

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Section: Relations With Other Shallow Water Type Modelsmentioning

confidence: 99%

“…Let us now consider the model introduced in [22], or, more precisely, its two dimensional extension presented in [11]. It reads…”

Section: Relations With Other Shallow Water Type Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

“…In section 1, we first detail similarities between Model (1) and other models mentioned in the Introduction, in particular [4,11,22]. Then we exhibit its main properties.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

Aguillon¹,

Audusse²,

Godlewski³

et al. 2018

SIAM J. Math. Anal.

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show abstract

“…Richard and Gavrilyuk [15] extended Dressler's roll-wave solutions to account for turbulent shear and dissipation. Reynolds' stresses are here related to enstrophy in the wave, providing wave-breaking as a model extension.…”

Section: Reviewmentioning

confidence: 99%

A Method of Chained Analytical Wave Structures for Large Scale Stratified Two-Phase Pipe Flows

Akselsen¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Pipeline transport systems can span vast distances, making finely resolved simulation techniques computationally unaffordable. This article examines the use of analytical steady wave solutions in a dynamic simulation framework as a technique for obtaining physical wave dynamics in a flow regime simulator without discretising individual wave structures. A scheme based on this principle is presented wherein a family of steady roll-waves profile solutions is generalised to allow for a dynamic profile evolution. These solutions are then implemented into a finite volume scheme where a wave solution constitutes a single dynamic grid cell. Waves interact dynamically to construct a wave regime evolving in time. Predictions on flow development are compared with finely resolved direct numerical simulations on fixed grids. Steady wave solutions, once subjected to coordinate stretching, behaves appropriately in the dynamic frame, predicting the regime development in time, the wave coalescences and the final steady state or slug transition. 806A.H. Akselsen

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A depth‐averaged two‐phase model for debris flows over erodible beds

Cao

et al. 2017

Earth Surf Processes Landf

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Mass exchange between debris flow and the bed plays a vital role in debris flow dynamics. Here a depth‐averaged two‐phase model is proposed for debris flows over erodible beds. Compared to previous depth‐averaged two‐phase models, the present model features a physical step forward by explicitly incorporating the mass exchange between the flow and the bed. A widely used closure model in fluvial hydraulics is employed to estimate the mass exchange between the debris flow and the bed, and an existing relationship for bed entrainment rate is introduced for comparison. Also, two distinct closure models for the bed shear stresses are evaluated. One uses the Coulomb friction law and Manning's equation to determine the solid and fluid resistances respectively, while the other employs an analytically derived formula for the solid phase and the mixing length approach for the fluid phase. A well‐balanced numerical algorithm is applied to solve the governing equations of the model. The present model is first shown to reproduce average sediment concentrations in steady and uniform debris flows over saturated bed as compared to an existing formula underpinned by experimental datasets. Then, it is demonstrated to perform rather well as compared to the full set of USGS large‐scale experimental debris flows over erodible beds, in producing debris flow depth, front location and bed deformation. The effects of initial conditions on debris flow mass and momentum gain are resolved by the present model, which explicitly demonstrates the roles of the wetness, porosity and volume of bed sediments in affecting the flow. By virtue of extended modeling cases, the present model produces debris flow efficiency that, as revealed by existing observations and empirical relations, increases with initial volume, which is enhanced by mass gain from the bed. Copyright © 2017 John Wiley & Sons, Ltd.

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A new model of roll waves: comparison with Brock’s experiments

Cited by 80 publications

References 23 publications

Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

A Method of Chained Analytical Wave Structures for Large Scale Stratified Two-Phase Pipe Flows

A depth‐averaged two‐phase model for debris flows over erodible beds

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