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The paper extends a stabilized fictitious domain finite element methodinitially developed for the Stokes problem to the incompressible Navier-Stokesequations coupled with a moving solid. This method presents the advantage topredict 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 interfacebetween the fluid and the structure is materialized by a level-set which cutsthe elements of the mesh. An algorithm is proposed in order to treat the timeevolution of the geometry and numerical results are presented on a classicalbenchmark of the motion of a disk falling in a channel.

A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid