## A computational framework for fluid-structure interaction: finite element formulation and applications.(English)Zbl 1155.76354

Summary: This work is concerned with the modelling of the interaction of fluid flow with flexible solid structures. The fluid flow considered is governed by the incompressible Navier-Stokes equations and modelled with stabilised low order velocity-pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. The structure is represented by means of an appropriate standard finite element formulation. For the temporal discretisation of both fluid and solid bodies, the discrete implicit generalised-$$\alpha$$ method is employed.
An important aspect of the presented work is the introduction of the independent interface discretisation, which allows an efficient, modular and expandable implementation of the solution strategy. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface.
The resulting strongly coupled set of non-linear equations is solved by means of a novel partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates the full linearisation of the overall incremental problem. Thus, asymptotically quadratic convergence of the residuals is achieved. Numerical examples are presented to demonstrate the robustness and efficiency of the methodology.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: