Geodesic
A penalty method for the simulation of fluid - rigid body interaction
João Janela1 ; Aline Lefebvre2 ; Bertrand Maury2
1 CEMAT, Instituto Superior Técnico and Departamento de Matemática, ISEG, Lisbon, Portugal;
2 Laboratoire de Mathématiques, Université Paris Sud, Orsay, France;
ESAIM. Proceedings, Tome 14 (2005), pp. 115-123.

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We present here a method to simulate the motion of a rigid body in a fluid. The method is based on a variational formulation on the whole fluid/solid domain, with some constraints on the unknown and the test functions. These constraints are relaxed by introducing a penalty term, which leads to a minimization problem over unconstrained functional spaces. This makes the method straightforward to implement from any finite element Stokes/Navier-Stokes solver. It is shown that, as the penalty parameter goes to infinity, we recover the coupled fluid-solid equations. We apply this approach to a simplified 2D model of the aortic valve.
DOI : 10.1051/proc:2005010

João Janela 1 ; Aline Lefebvre 2 ; Bertrand Maury 2

1 CEMAT, Instituto Superior Técnico and Departamento de Matemática, ISEG, Lisbon, Portugal;
2 Laboratoire de Mathématiques, Université Paris Sud, Orsay, France; 
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     author = {Jo\~ao Janela and Aline Lefebvre and Bertrand Maury},
     title = {A penalty method for the simulation of fluid - rigid body interaction},
     journal = {ESAIM. Proceedings},
     pages = {115--123},
     publisher = {mathdoc},
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     year = {2005},
     doi = {10.1051/proc:2005010},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2005010/}
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João Janela; Aline Lefebvre; Bertrand Maury. A penalty method for the simulation of fluid - rigid body interaction. ESAIM. Proceedings, Tome 14 (2005), pp. 115-123. doi : 10.1051/proc:2005010. http://geodesic.mathdoc.fr/articles/10.1051/proc:2005010/

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