# A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari; Fausto Saleri

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 2, page 211-234
- ISSN: 0764-583X

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topFerrari, Stefania, and Saleri, Fausto. "A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography." ESAIM: Mathematical Modelling and Numerical Analysis 38.2 (2010): 211-234. <http://eudml.org/doc/194211>.

@article{Ferrari2010,

abstract = {
The motion of an incompressible fluid confined to a shallow basin with
a slightly varying bottom topography is considered. Coriolis force,
surface wind and pressure stresses, together with bottom and
lateral friction stresses are taken into account. We introduce
appropriate scalings into a three-dimensional anisotropic eddy
viscosity model; after averaging on the vertical direction and
considering some asymptotic assumptions, we obtain a two-dimensional
model, which approximates the three-dimensional model at the second
order with respect to the ratio between the vertical scale and the
longitudinal scale. The derived model is shown to be symmetrizable
through a suitable change of variables. Finally, we propose some
numerical tests with the aim to validate the proposed model.
},

author = {Ferrari, Stefania, Saleri, Fausto},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Navier-Stokes equations; Saint Venant equations; free surface flows.},

language = {eng},

month = {3},

number = {2},

pages = {211-234},

publisher = {EDP Sciences},

title = {A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography},

url = {http://eudml.org/doc/194211},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Ferrari, Stefania

AU - Saleri, Fausto

TI - A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 2

SP - 211

EP - 234

AB -
The motion of an incompressible fluid confined to a shallow basin with
a slightly varying bottom topography is considered. Coriolis force,
surface wind and pressure stresses, together with bottom and
lateral friction stresses are taken into account. We introduce
appropriate scalings into a three-dimensional anisotropic eddy
viscosity model; after averaging on the vertical direction and
considering some asymptotic assumptions, we obtain a two-dimensional
model, which approximates the three-dimensional model at the second
order with respect to the ratio between the vertical scale and the
longitudinal scale. The derived model is shown to be symmetrizable
through a suitable change of variables. Finally, we propose some
numerical tests with the aim to validate the proposed model.

LA - eng

KW - Navier-Stokes equations; Saint Venant equations; free surface flows.

UR - http://eudml.org/doc/194211

ER -

## References

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## Citations in EuDML Documents

top- Emmanuel Audusse, Marie-Odile Bristeau, Finite-volume solvers for a multilayer Saint-Venant system
- Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame, Jacques Sainte-Marie, 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, A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

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