Numerical Solution of the FLow Past a Freely Oscillating Body in Waves and Current

The uid-structure interaction due to the ow past a circular cylinder is studied in order to analyze the hydrodynamic loads and the related body motions. The cilinder is restrained to in-line displacements while cross-fl ow oscillations are possible through a spring-damper system. After assuming an incompressible laminar ow, the solution of the uid dynamic problem is achieved through a fractional step algorithm where a particle method with a deterministic diusion scheme is used for the dynamics of the vorticity. The uid velocity is expressed by an integral representation formula in terms of the vorticity eld and of the velocity itself at the boundaries. The relevant integral equation are solved via an N logN algorithm and the computed tangential velocity at the solid boundary allows for the generation of vorticity in order to satisfy the no{slip condition. A fast summation technique for the rapid evaluation of the velocity is adopted. The investigated range of the Reynolds number (from 95 to 135) shows that, within the lock-in range, the vortex shedding frequency coincides with the natural frequency in still water and that large body displacements occur.