Efficient time domain response computation of massive wave power farms

A potential future challenge in the wave energy sector will involve the design and construction of massive wave power farms. That is, collections of several (> 100) wave energy converters (WEC) operating in identical environmental conditions at a distance comparable with typical water wave lengths. In this context, the WECs are likely to be influenced by each another by radiation force effects that are associated with the radiated wave field propagated by WECs operating in the surrounding wave field. These effects are commonly captured by the Cummins’ equation, where the radiation force is expressed as a convolution integral depending on the past values of the WEC response. Due to this mathematical representation, the time domain computation of the wave farm response can become computationally daunting. This article proposes one approach for computing efficiently the wave farm response in the time domain. Specifically, it demonstrates that the values of the radiation force components can be determined at each time step from their previous values by approximating the retardation function matrix elements via the Prony method. A notable advantage of this approach with respect to the ones available in the open literature is that it does not require either the storage of past response values or additional differential equations. Instead, it uses simple algebraic expressions for updating at each time instant the radiation force values. Obviously, this feature can induce significant computational efficiency in analyzing an actual wave farm facility. The reliability and efficiency of the proposed algorithm are assessed vis-à-vis direct time domain comparisons and Monte Carlo data concerning a wave farm composed by an array of U-Oscillating Water Columns. Notably, the proposed methodology can be applied to any linear or nonlinear dynamics problem governed by differential equations involving memory effects.