Numerical aspects and controllability of a one dimensional fluid-structure model

In this paper we summarize some recent results from Cîndea et al. (2013) concerning the controllability of a one dimensional fluid-structure model. These results are confirmed by numerical experiments in some particular cases. More precisely, we consider a simplified model for a point swimmer moving, according to Newton's law, in an one dimensional fluid which is modeled by the viscous Burgers equation. The control variable is the relative velocity of the swimmer with respect to the fluid. The main result of the paper gives the conditions in which we can drive the fluid and the velocity of the point mass to zero. A set of reachable positions of the point mass is also obtained. From the numerical point of view, we compute the L2-minimal norm control for a linearized and simplified model. The method we used combine a finite elements discretization in space, a finite-difference centered scheme in time and the conjugate gradient method.