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A complete and consistent second-order hydrodynamic model for floating structures with large horizontal motions

Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making the traditional formulations in an inertial coordinate system inconsistent and less applicable. To address this issue, we explore an alternative formulation completely based on a non-inertial body-fixed coordinate system. Unlike the traditional seakeeping models, this formulation consistently allows for large-amplitude horizontal motions. A numerical model based on a higher-order boundary element is applied to solve the resulting boundary-value problems in the time domain. A new set of explicit time-integration methods, which do not necessitate the use of upwind schemes for spatial derivatives, are designed to deal with the convectivetype free-surface conditions. To suppress the weak saw-tooth instabilities on the free surface in time marching, we also present novel low-pass filters based on optimized weighted-least-squares, which are in principle applicable for both structured and unstructured meshes. For ship seakeeping and added resistance analyses, we show that the present computational model does not need to use softsprings for surge and sway, in contrast to the traditional models. For a spar floating offshore wind turbine (FOWT), the importance of consistently taking into account the effects of large horizontal motions is demonstrated considering the bichromatic incident waves. The present model is also referred to as a complete 2nd order wave-load model, as all the 2nd order wave loads, including the sumfrequency and difference-frequency components, are solved simultaneously.