| A Numerical study has been conducted into vortex-induced vibrations of an elastic circular cylinder, using the arbitrary Lagrangian-Eulerian Formulation (ALE) and the domain decomposition method (DDM). The ALE formulation is a generalized concept to deal with the problem of moving boundaries around a continuum, and the DDM method is advantageous to solve such complicated flow problem. The fluid motion is described by the incompressible Navier-Stokes (N-S) equations, and the cylinder motion is modeled by a spring-damper-mass system. The primitive variable and pressure Poisson equation formulation is employed for the numerical solution of the N-S equations, in tensor forms, on an H-0 type of non-staggered grids that makes it convenient to apply a strict inflow and outflow boundary condition. The non-linear fluid-structure interaction is simulated numerically by solving the N-S equations, the pressure equation and the cylinder motion' equation in turn for every time step. The N-S equation' s convection term and dissipation term are discretized using the third-order upwind compact scheme and the fourth-order central compact scheme, respectively. The cylinder motion' equation is solved using the Runge-Kutta method.By numerous computational data, we successfully captured the "locked-in" , "beat" and "phase switch" phenomena, and the present discusses in detail the vortex structure, the unsteady lift and drag on the cylinder, and the cylinder' s displacement at various conditions of the frequency ratio, the mass ratio and the damp coefficient in a low Reynolds' range. The results about the one-degree-of-freedom model and two-degree-of-freedom model are compared; the comparison shows the streamwise motion of the body does influence the vortex-induced variations, even though the transverse motion is dominant for a bluff body in a cross-flow. Besides, a 3-D numerical simulation of uniform flow pasta sphere is presented, that prepares for the investigation of 3-D vortex-induced vibrations.
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