# 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

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- 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 45.1 (2011): 169-200. <http://eudml.org/doc/197421>.

@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},

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

language = {eng},

month = {1},

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/197421},

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

DA - 2011/1//

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/197421

ER -

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