We present numerical results for vibration responses of two circular cylinders which move to in-line and cross-flow directions along a smooth flow, and which are arranged at a spacing larger than the critical spacing of the centre-to-centre of the cylinders. When the Scruton number is low, it is well- known that two kinds of in-line vibrations, named first- and second-excited vibrations, occur in the range of low reduced velocities. On the other hand, when the reduced velocity exceeds approximately 5, it has been reported from many experimental data that the vortex-induced vibration (VIV) was observed in the wide range of the reduced velocity. In order to capture such vibration responses, numerical computations of the Navier-Stokes equations are carried out by means of the Petrov-Galerkin type finite element method and the arbitrary Lagrangian-Eulerian method. In addition, the numerical solution stabilization of the Navier-Stokes equations is performed by the third-order upwind scheme. From our numerical results, we discuss the response mechanisms of the cylinders in detail.
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