This paper presents the mathematical modeling and numerical methodology performed prior to the prototype deployment of the AquaBuOY, one of the few wave energy devices that have reached the ocean deployment stage. The combination of numerical computations, and laboratory testing produced some encouraging findings about how the AquaBuOY responds to real wave conditions. However, it also highlighted deficiencies in some of the early modeling, which emphasized the need for a time domain model in realistic wave conditions that includes accurate hydrodynamic and drag coefficients.
This paper focuses on the governing equations that model the vertical dynamics of the AquaBuOY and the numerical solutions of these equations in order to predict the absorbed power of the device. Numerical results are presented in the time domain for both regular and irregular wave regimes (realistic wave conditions) as well as compared to experimental data in a regular wave regime.

While the two body system is challenging to model, due to the inclusion of variables such as the wave forcing term as well as identifying the non linear damping term along with a linear spring term needed to model the power takeoff system, it does provide a robust tool for wave energy research.