A stabilized Arlequin formulation for fluid-structure interaction analysis

Resumo

Fluid-structure interactions are multi-physical problems which may present complex coupled and local-
ized phenomena. In the literature, most of the methods for these rely in two main approaches: interface tracking

and interface capturing families of methods. In the interface tracking methods, fluid and solid discretizations are
conform to the fluid-structure interface and its location is a part of the solution, requiring an additional step (mesh
moving or re-mesh) when it changes. On the other hand, interface capturing methods employ immersed boundary
techniques to describe the fluid-structure interface position in an Eulerian domain. In this work, an alternative

approach is presented. Frame structures with Timoshenko-Reissner kinematics are modeled in the positional ver-
sion of the finite element method, a simple alternative for the simulation of nonlinear dynamic problems. The

fluid, described by the incompressible Navier-Stokes equations, is modeled in the Arlequin framework, a domain
decomposition method based on the superposition of a local model (located in a particular region of interest) to
a global one, unsuitable to capture the localized effects. The communication between models is provided by a
Lagrange multiplier field, defined in a subset of the overlapping zone. This strategy has been applied successfully

for the simulation of incompressible flow problems with fixed overlapped models, i.e., in an Eulerian descrip-
tion. In this work, the methodology is extended to an Eulerian-ALE version, covering the case of a moving local

model, applicable to the simulation of fluid-structure interactions involving large structural displacements. The
resulting model is coupled by a strong Dirichlet-Neumann partitioned scheme with Aitken’s relaxation. Finally,
flexibility and accuracy of our technique are evaluated by numerical tests. As main advantages, one can point the
flexibility on the treatment of problems with large rigid body motion, such as turbines and rotors (a drawback of
interface tracking methods, that sometimes requires re-meshing steps), while keeps a suitable discretization close
to the fluid-structure interface throughout the analysis (not always possible when interface capturing methods are
employed).