A multilayer Saint-Venant model: Derivation and numerical validation

Audusse, Emmanuel

doi:10.3934/dcdsb.2005.5.189

Cited by 101 publications

(104 citation statements)

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“…Each layer is assumed to have a constant density, ρ i , i = 1, 2 (ρ 1 < ρ 2 ). The unknowns q i (x, t) and h i (x, t) represent respectively the mass-flow and the thickness of the ith layer at the section of coordinate x at time t. The numerical resolution of two-layer or multilayer shallow water systems has been object of an intense research during the last years: see for instance [1], [3], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [17], [22], [24] . .…”

Section: Introductionmentioning

confidence: 99%

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

2011

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The goal of this article is to design a new approximate Riemann solver for the two-layer shallow water system which is fast compared to Roe schemes and accurate compared to Lax-Friedrichs, FORCE, or GFORCE schemes (see [14]). This Riemann solver is based on a suitable decomposition of a Roe matrix (see [27]) by means of a parabolic viscosity matrix (see [16]) that captures some information concerning the intermediate characteristic fields. The corresponding first order numerical scheme, which is called IFCP (Intermediate Field Capturing Parabola) is linearly L ∞ -stable, well-balanced, and it doesn't require an entropy-fix technique. Some numerical experiments are presented to compare the behavior of this new scheme with Roe and GFORCE methods.

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Section: Introductionmentioning

confidence: 99%

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

2011

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“…In the multilayer Saint-Venant system derived by Audusse et al in [3] the layers are assumed to be advected by the flow. Then, no mass exchange occurs between neighboring layers making the model physically closer to non-miscible fluids simulation.…”

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confidence: 99%

A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution

2013

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In this work we present a mutilayer approach to the solution of non-stationnary 3D Navier-Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulation and by considering a reduced family of test functions. The procedure naturally provides the mass and momentum interfaces conditions. The mass and momentum conservation across interfaces is formulated via normal flux jump conditions. The jump conditions associated to momentum conservation are formulated by means of an approximation of the vertical derivative of the velocity that appears in the stress tensor. We approximate the multilayer model for hydrostatic pressure, by using a PVM finite volume scheme and we present some numerical tests that show the main advantages of the model: it improves the approximation of the vertical velocity, provides good predictions for viscous effects and simulates re-circulations behind solid obstacles.

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“…By planar Riemann problem, we mean the case of an initial data which is constant by half-plane, i.e. (2) ∀(x, y) ∈ R 2 , (h, U, U)(0,…”

Section: Introductionmentioning

confidence: 99%

“…Such layerwise models were introduced as a way to approximate the three dimensional hydrostatic Euler equations by using two dimensional models, but avoiding the shallow flow hypothesis. Different models can be derived, depending on the closure that is chosen for the definition of the layer, see [2,21]. Other multilayer models was proposed in the literature for stratified flow [17,20] but does not enter in the scope of this work.…”

Section: Introductionmentioning

confidence: 99%

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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A multilayer Saint-Venant model: Derivation and numerical validation

Cited by 101 publications

References 0 publications

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution

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

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