A complete and consistent second-order hydrodynamic model in the time domain 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 extend and 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 adopted to deal with the convective-type free-surface conditions. To suppress the weak saw-tooth instabilities on the free surface in time marching, novel low-pass filters based on optimized weighted-least-squares are also developed, which are 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 soft-springs for surge and sway, in contrast to the traditional models. The present model is considered as a complete 2nd order wave-load model, as all the 2nd order wave loads, including the sum-frequency and difference-frequency components, are solved simultaneously. Some more details on the model can be found in two recent paper by Zheng et al. (2020) and Shao et al. (2022).

At the end of the lecture, two examples, including a floating monopile and the OC5 floating offshore wind turbine, both exposed to irregular waves, will be studied using the new solver for demonstration purposes.