Vertical-axis wind turbines (VAWTs) are becoming popular in the offshore wind energy field due to their superiority over horizontal-axis wind turbines (HAWTs) on a floating platform. Though they are more stable and easier to service than HAWTs, a single VAWT must have a more complex mooring system. A novel platform has been designed and will be tested at a model-scale using hybrid simulation. This type of simulation combines the advantages of both the experimental and computational domains, which is necessary for such a model that is subject to varying winds and waves. In order to simulate the aerodynamics of the turbines, a high-order discontinuous Galerkin ILES method is first used to estimate the forces on a single airfoil in 2D and 3D over large angles of attack at low chord Reynolds numbers. This methodology is also applied to rotating wind turbines undergoing prescribed motion. The forces on the blades are compared to experimental data as well as analytical turbine models. Finally, some results from a moving mesh method using an element flipping technique are shown. The talk is based on joint work with Per-Olof Persson and Luming Wang (UC Berkeley).