A consistent second-order hydrodynamic model in the time domain for floating structures with large horizontal motions

TL;DR

This paper develops a second-order hydrodynamic model in the time domain using a non-inertial coordinate system, enabling accurate simulation of large horizontal motions of floating structures, with improved numerical stability and applicability.

Contribution

It introduces a novel non-inertial coordinate formulation for second-order hydrodynamics, along with explicit time-integration and low-pass filtering techniques for better simulation of large motions.

Findings

The model accurately captures large horizontal motions in floating structures.

It eliminates the need for soft-springs in surge and sway for seakeeping analysis.

The approach effectively computes all second-order wave loads simultaneously.

Abstract

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 recently developed 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, we also present novel low-pass filters based on optimized weighted-least-squares, which are in principle applicable for both structured and unstructured meshes. The presented schemes for the convection equation and the low-pass filter are also relevant for other engineering fields dealing with similar mathematical problems. 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. For a floating monopile, the importance of consistently taking into account the effects of large horizontal motions is demonstrated considering the bi-chromatic incident waves. 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.