# A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

Emmanuel Audusse; Marie-Odile Bristeau; Benoît Perthame; Jacques Sainte-Marie

- Volume: 45, Issue: 1, page 169-200
- ISSN: 0764-583X

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topAudusse, Emmanuel, et al. "A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.1 (2011): 169-200. <http://eudml.org/doc/273147>.

@article{Audusse2011,

abstract = {The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.},

author = {Audusse, Emmanuel, Bristeau, Marie-Odile, Perthame, Benoît, Sainte-Marie, Jacques},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Navier-Stokes equations; Saint-Venant equations; free surface; multilayer system; kinetic scheme},

language = {eng},

number = {1},

pages = {169-200},

publisher = {EDP-Sciences},

title = {A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation},

url = {http://eudml.org/doc/273147},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Audusse, Emmanuel

AU - Bristeau, Marie-Odile

AU - Perthame, Benoît

AU - Sainte-Marie, Jacques

TI - A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 1

SP - 169

EP - 200

AB - The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.

LA - eng

KW - Navier-Stokes equations; Saint-Venant equations; free surface; multilayer system; kinetic scheme

UR - http://eudml.org/doc/273147

ER -

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