Geodesic
A fictitious domain approach for Fluid-Structure Interactions based on the eXtended Finite Element Method.
Sébastien Court1 ; Michel Fournié2 ; Alexei Lozinski3
1 Université Blaise Pascal, Laboratoire de Mathématiques, Campus des Cézeaux, B.P. 80026, 63171 Aubière Cedex France;
2 Université de Toulouse, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 TOULOUSE Cedex;
3 Université de Franche-Comté, Laboratoire de Mathématiques de Besançon, 16 route de Gray, 25030 Besançon Cedex;
ESAIM. Proceedings, Tome 45 (2014), pp. 308-317.

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In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the Poisson problem. The fluid part is treated by a mixed finite element method, and a Dirichlet condition is imposed by a Lagrange multiplier on an immersed structure localized by a level-set function. A stabilization technique is carried out in order to get the convergence for this multiplier. The latter represents the forces that the fluid applies on the structure. The aim is to perform fluid-structure simulations for which these forces have a central role. We illustrate the capacities of the method by extending it to the incompressible Navier-Stokes equations coupled with a moving rigid solid.
DOI : 10.1051/proc/201445032

Sébastien Court 1 ; Michel Fournié 2 ; Alexei Lozinski 3

1 Université Blaise Pascal, Laboratoire de Mathématiques, Campus des Cézeaux, B.P. 80026, 63171 Aubière Cedex France;
2 Université de Toulouse, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 TOULOUSE Cedex;
3 Université de Franche-Comté, Laboratoire de Mathématiques de Besançon, 16 route de Gray, 25030 Besançon Cedex; 
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     author = {S\'ebastien Court and Michel Fourni\'e and Alexei Lozinski},
     title = {A fictitious domain approach for {Fluid-Structure} {Interactions} based on the {eXtended} {Finite} {Element} {Method.}},
     journal = {ESAIM. Proceedings},
     pages = {308--317},
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     doi = {10.1051/proc/201445032},
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Sébastien Court; Michel Fournié; Alexei Lozinski. A fictitious domain approach for Fluid-Structure Interactions based on the eXtended Finite Element Method.. ESAIM. Proceedings, Tome 45 (2014), pp. 308-317. doi : 10.1051/proc/201445032. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445032/

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