Tidal energy is now considered as a renewable power source worldwide that can be used to reduce global warming. In order to harvest the tidal current power, horizontal and vertical axis tidal turbines (VATTs) have recently received increasing interests. To implement the detailed design process, the power outputs of 2D and 3D VATTs are simulated by a novel fidelity fluid-structure turbulence model in this work. This model is capable of simulating the fluid dynamics of the turbulent flow, as well as the stress, vibration, deformation, and motion of structures. Most importantly, flow-induced vibration for 3D VATTs is modelled by this model. In order to improve the computational efficiency, a large aspect ratio anisotropic mesh adaptivity is used to speed up simulations. The simulation results of these complex practical test cases are all in good agreement with experimental and numerical data in the literature. The model can be used to accurately predict the power output of VATTs, which can help to choose design configurations with high power output efficiency. More importantly, this model can be used to predict the flow-induced vibration of 3D VATTs, which can help to design VATTs with low vibration. Finally, the comparison between flexible and rigid VATTs shows the advantages of this model which demonstrates its capabilities when analysing the elasticities for realistic VATTs.