A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow

Abstract

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.