A fixed point algorithm is proposed to solve a fluid-structure interaction problem with the supplementary constraint that the structure displacements are limited by a rigid obstacle. Fictitious domain approach with penalization is used for the fluid equations. The surface forces from the fluid acting on the structure are computed using the fluid solution in the structure domain. The continuity of the fluid and structure velocities is imposed through the penalization parameter. The constraint of non-penetration of the elastic structure into the rigid obstacle is treated weakly. A convex constrained optimization problem is solved in order to get the structure displacements. Numerical results are presented.

An implicit scheme by partitioned procedures is proposed to solve a dynamic fluid–structure interaction problem in the case when the structure displacements are limited by a rigid obstacle. For the fluid equations (Sokes or Navier–Stokes), the fictitious domain method with penalization was used. The equality of the fluid and structure velocities at the interface was obtained using the penalization technique. The surface forces at the fluid–structure interface were computed using the fluid solution in the structure domain. A quadratic optimization problem with linear inequalities constraints was solved to obtain the structure displacements. Numerical results are presented.