Abstract
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.
Highlights
The Arbitrary Lagrangian Eulerian (ALE) method was successfully employed for solving fluid–structure interaction problems, see [1]
In [18], the fictitious domain method with penalization presented in [19,20] was used in order to handle the contact between a linear elastic structure and a rigid obstacle in a fluid–structure interaction problem
The surface forces at the fluid–structure interface were computed using the fluid solution in the structure domain
Summary
The Arbitrary Lagrangian Eulerian (ALE) method was successfully employed for solving fluid–structure interaction problems, see [1]. A monolithic Eulerian framework with remeshig was used in [14], a stabilised immersed methodology on hierarchical b-spline grids was employed in [15], the cut finite element method was used in [16], a Nitsche-based formulation with artificial fluid in the gap between structure and obstacle was presented in [17]. In [18], the fictitious domain method with penalization presented in [19,20] was used in order to handle the contact between a linear elastic structure and a rigid obstacle in a fluid–structure interaction problem. We present a dynamic fluid–structure interaction problem when the elastic structure is in contact with a rigid obstacle. The fluid was modeled by the Stokes as well as by the Navier–Stokes equations
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