Geodesic
Hydromorpho: A coupled model for unsteady Stokes/Exner equations and numerical results with Feel++ library
Nora Aïssiouene1 ; Tarik Amtout2 ; Matthieu Brachet3 ; Emmanuel Frenod4 ; Romain Hild5 ; Christophe Prud’homme5 ; Antoine Rousseau6 ; Stephanie Salmon7
1 Inria - CEREMA - Sorbonne Universités, UPMC Univ Paris 06 - CNRS, UMR 7598, Laboratoire Jacques-Louis Lions
2 Faculté des Sciences et Techniques Tanger, Maroc
3 Institut Elie Cartan de Lorraine, Université de Lorraine, Site de Metz, Bât. A Ile du Saulcy, F-57045 Metz Cedex 1  
4 Université Bretagne-Sud, LMBA UMR 6205, Vannes
5 Institut de Recherche Mathématique Avancée, Strasbourg
6 Inria and Institut Montpelliérain Alexander Grothendieck, Team LEMON, Bat 5 - CC05 017, 860 rue Saint-Priest, 34095 Montpellier Cedex 5, France
7 Laboratoire de Mathématiques de Reims, Fédération ARC CNRS 3399, Université de Reims Champagne-Ardenne
ESAIM. Proceedings, Tome 55 (2016), pp. 23-40.

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We propose to couple the Exner equation with the Stokes equations to model the bedload sediment in geophysical flows . This work is a preliminary study to directly model the hydrodynamic flow by the unsteady Stokes equation instead of the classical shallow water equation. We focus in this proceeding on the coupling applying fluid structure interaction approach to morphodynamical behavior. In other words, we follow the approach of fluid interaction models replacing the structure equation by the Exner equation. The aim of this work is to validate the proposed procedure. These equations are solved by finite element method using the library FEEL++.
DOI : 10.1051/proc/201655023

Nora Aïssiouene 1 ; Tarik Amtout 2 ; Matthieu Brachet 3 ; Emmanuel Frenod 4 ; Romain Hild 5 ; Christophe Prud’homme 5 ; Antoine Rousseau 6 ; Stephanie Salmon 7

1 Inria - CEREMA - Sorbonne Universités, UPMC Univ Paris 06 - CNRS, UMR 7598, Laboratoire Jacques-Louis Lions
2 Faculté des Sciences et Techniques Tanger, Maroc
3 Institut Elie Cartan de Lorraine, Université de Lorraine, Site de Metz, Bât. A Ile du Saulcy, F-57045 Metz Cedex 1  
4 Université Bretagne-Sud, LMBA UMR 6205, Vannes
5 Institut de Recherche Mathématique Avancée, Strasbourg
6 Inria and Institut Montpelliérain Alexander Grothendieck, Team LEMON, Bat 5 - CC05 017, 860 rue Saint-Priest, 34095 Montpellier Cedex 5, France
7 Laboratoire de Mathématiques de Reims, Fédération ARC CNRS 3399, Université de Reims Champagne-Ardenne 
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     author = {Nora A{\"\i}ssiouene and Tarik Amtout and Matthieu Brachet and Emmanuel Frenod and Romain Hild and Christophe Prud{\textquoteright}homme and Antoine Rousseau and Stephanie Salmon},
     title = {Hydromorpho: {A} coupled model for unsteady {Stokes/Exner} equations and numerical results with {Feel++} library},
     journal = {ESAIM. Proceedings},
     pages = {23--40},
     publisher = {mathdoc},
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     year = {2016},
     doi = {10.1051/proc/201655023},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201655023/}
}
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Nora Aïssiouene; Tarik Amtout; Matthieu Brachet; Emmanuel Frenod; Romain Hild; Christophe Prud’homme; Antoine Rousseau; Stephanie Salmon. Hydromorpho: A coupled model for unsteady Stokes/Exner equations and numerical results with Feel++ library. ESAIM. Proceedings, Tome 55 (2016), pp. 23-40. doi : 10.1051/proc/201655023. http://geodesic.mathdoc.fr/articles/10.1051/proc/201655023/

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