Numerical simulations of 3D free surface flows by a multilayer Saint‐Venant model

Audusse, Emmanuel; Bristeau, Marie-Odile; Decoene, Astrid

doi:10.1002/fld.1534

Cited by 34 publications

(49 citation statements)

References 9 publications

(17 reference statements)

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“…The viscosity μ, the friction coefficient κ and the derivative of the bottom topography Z(x) are of the order of . We refer to (Ferrari and Saleri, 2004;Gerbeau and Perthame, 2001) for the derivation of the classical Saint-Venant system and to (Audusse, 2005;Audusse et al, 2006a;Audusse et al, 2007) for the derivation of the multilayer Saint-Venant system. In the next subsection we shall recall important properties of both systems and explain the choice of the particular form of the multilayer Saint-Venant system that we consider.…”

Section: Saint-venant Type Systemsmentioning

confidence: 99%

“…The non-conservative pressure source term of the momentum equation (5) is treated explicitly in a finite volume framework. We refer the reader to (Audusse et al, 2006a;Audusse et al, 2007) for more details. The viscous source term is computed implicitly.…”

Section: Numerical Applicationsmentioning

confidence: 99%

“…It allows us to consider nonconstant velocities along the vertical direction (that is the main restriction of the classical SaintVenant system) while keeping the computational advantages of the classical Saint-Venant system (robustness, efficiency, etc.). It was proved to be a relevant alternative to the use of hydrostatic Navier-Stokes equations (Audusse et al, 2006a;Audusse et al, 2007). Some new source terms appear in the multilayer Saint-Venant system.…”

Section: Introductionmentioning

confidence: 99%

“…Some new source terms appear in the multilayer Saint-Venant system. In particular, it includes a nonconservative pressure source term that involves some numerical difficulties (Audusse, 2005;Audusse et al, 2006a;Audusse et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

“…More recently some attention has also been paid to the treatment of the Coriolis source term (Audusse et al, 2006b;Bouchut et al, 2004). We also mention that the pressure source term of the multilayer SaintVenant system has to be discretized carefully (Audusse et al, 2006a;Audusse et al, 2007).…”

mentioning

confidence: 99%

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Finite-Volume Solvers for a Multilayer Saint-Venant System

Audusse¹,

Bristeau²

2007

International Journal of Applied Mathematics and Computer Science

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We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

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Section: Saint-venant Type Systemsmentioning

confidence: 99%

Section: Numerical Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Finite-Volume Solvers for a Multilayer Saint-Venant System

Audusse¹,

Bristeau²

2007

International Journal of Applied Mathematics and Computer Science

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A kinetic interpretation of the section‐averaged Saint‐Venant system for natural river hydraulics

Goutal¹,

Sainte-Marie

2010

Numerical Methods in Fluids

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SUMMARYThe classical Saint-Venant system is well suited for the modeling of dam breaks, hydraulic jumps, reservoir emptying, flooding etc. For many applications, the extension of the Saint-Venant system to the case of non-rectangular channels is necessary and this section-averaged Saint-Venant system exhibits additional source terms. The main difficulty of these equations consists of the discretization of these source terms.In this paper we propose a kinetic interpretation for the section averaged Saint-Venant system and derive an associated numerical scheme. The numerical scheme-2nd order in space and time-preserves the positivity of the water height, and is well-balanced. Numerical results including comparisons with analytic and experimental test problems illustrate the accuracy and the robustness of the numerical algorithm.

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Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

Xia¹,

Benedicenti

Field³

2013

Numerical Methods in Fluids

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SUMMARYA new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles.To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved.Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.

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Numerical simulations of 3D free surface flows by a multilayer Saint‐Venant model

Cited by 34 publications

References 9 publications

Finite-Volume Solvers for a Multilayer Saint-Venant System

Finite-Volume Solvers for a Multilayer Saint-Venant System

A kinetic interpretation of the section‐averaged Saint‐Venant system for natural river hydraulics

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

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