In this work, a frequency-domain method for the numerical solution of the nonlinear dynamics of a wave energy converter with a pumping system is presented. To this end, a finite Fourier series is used to describe the nonlinear force components, i.e., the pumping force. The dynamics of the buoy and the piston are obtained by solving a set of linear motion equations. The numerical model is validated by comparing it with experimental results. The dynamic characteristics of the pumping system are investigated by performing a series of numerical simulations for several approximation orders under various wave conditions. The advantages and limitations of this method are also discussed in the paper. This work provides great insight into the mechanism of a WEC with a pumping unit under various sea states, which can guide the design of a multi-piston pump (MPP) system. This model will be applied to investigate the optimal configuration for the MPP system in the future.

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