## A computational framework for fluid-rigid body interaction: finite element formulation and applications.(English)Zbl 1123.76029

Summary: This work is concerned with the modelling of interaction of fluid flow with flexibly supported rigid bodies. The fluid flow is governed by incompressible Navier-Stokes equations and modelled by employing stabilised low-order velocity-pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian strategy. The rigid body motion, excited by the fluid flow, is restricted by elastic and damping properties of the supports. For the temporal discretisation, the discrete implicit generalised-$$\alpha$$ method is employed. The resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure, which is based on Newton-Raphson methodology and incorporates full linearisation of the overall incremental problem. The strong coupling is resolved and optimal convergence of the residuals is achieved. Several numerical examples demonstrate the robustness and efficiency of the methodology. The examples clearly capture the phenomena of vortex-induced oscillations and galloping.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 70E99 Dynamics of a rigid body and of multibody systems
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