  The paper extends a stabilized fictitious domain finite element method
initially developed for the Stokes problem to the incompressible Navier-Stokes
equations coupled with a moving solid. This method presents the advantage to
predict an optimal approximation of the normal stress tensor at the interface.
The dynamics of the solid is governed by the Newton's laws and the interface
between the fluid and the structure is materialized by a level-set which cuts
the elements of the mesh. An algorithm is proposed in order to treat the time
evolution of the geometry and numerical results are presented on a classical
benchmark of the motion of a disk falling in a channel.
