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

Abstract

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.