A penalty method for the simulation of fluid - rigid body interaction

Joao Janela (1) , Aline Lefebvre (2) , Bertrand Maury (2) , Aline Lefebvre-Lepot (2)

1 CEMAT - Center for Computacional and Stochastic Mathematics
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Navier-Stokes equation; rigid motion; finite element; penalty method; valve

Domaines: Analyse numérique [math.NA]

Joao Janela, Aline Lefebvre, Bertrand Maury, Aline Lefebvre-Lepot. A penalty method for the simulation of fluid - rigid body interaction. ESAIM: Proceedings and Surveys, 2005, 14, pp.115-123. ⟨hal-00728372⟩