Mathematics

Due to the gradual depletion of oil and gas resourcesonshore and in shallow waters during the last years there is anincreasing interest in deeper waters, where a large part of theremaining oil and gas is located. This recent interest in deeperwaters is coming not only from the petroleum industry but also fromthe renewable energy sector. The sea, especially in deep waters, has ahuge energy potential,  which could be exploited using wave energyconverters, solar power plants and wind turbines located on offshoreplatforms. Long slender cylinders are found in many offshoreapplications and are the representative system for mooring lines,risers, umbilicals, and free spanning pipelines in deep water. Theresponse of this kind of structures due to wave, current, and tideloads may be complex, and phenomena such as vortex induced vibrations(VIV), unsteady lock-in, dual resonance, and travelling waves responsemay occur. Much progress has been made to understand the VIVphenomenon, but an efficient and reliable model is still missing inliterature. Computational fluid dynamics (CFD) methods, especiallyconsidering the increase of the available computational power, havedemonstrated to be a possible way to get the response of flexiblestructures in an offshore environment, but they are still notapplicable for long term simulations and for simulations in fullscale. The response of a small scale model, which is already flexible,is studied under different imposed motions using a high-fidelity fluidstructure interaction (FSI) solver. This solver has been developed bycoupling a CFD finite volume solver with a structural finite elementsolver. The results of this high fidelity model are used to develop areduced order model (ROM). The so developed ROM, consisting in thecombination of a wake oscillator model and a state space model, isable to capture both the in-line and the cross-flow response of thestructure. Comparisons with experimental activities in full scale are presented and discussed.