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A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow. (English) Zbl 1425.74156
Summary: We present a stable partitioned iterative scheme for solving fluid-body interaction problems at low structure-to-fluid mass ratio. The scheme relies on the so-called nonlinear interface force correction based on Aitken’s extrapolation process to stabilize the coupled partitioned system employing an arbitrary Lagrangian-Eulerian finite element framework. Approximate interface force correction is constructed through subiterations to account for the missing effects of off-diagonal Jacobian terms in the partitioned staggered scheme. Through the generalized Aitken’s geometric extrapolation process with a dynamic stabilization parameter, the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid-structure interaction with strong added-mass effects. To assess the proposed iterative scheme against the standard strong coupling, effects of mass ratio are investigated for a freely vibrating circular cylinder. We show that our second-order scheme is stable for low mass density ratio and hence is able to handle strong added-mass effects. The numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake-induced vibration and galloping.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
Software:
METIS
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