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

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 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.

Resonant response of a flexible semi-submersible floating structure: experimental analysis and second-order modelling

“…Drift force terms of the form F ∝ f (ξ (1) η (1) ), corresponding to a first-order force applied in the deformed state, are suspected to cause this discrepancy, but are not implementable in the present linear response model. Shao et al (2021) suggest that large-amplitude horizontal responses to low-frequency forcing lead to inaccuracy in force models that are evaluated in the equilibrium position only and argue that force calculation in the displaced body-fixed coordinate system will accurately resolve the sub-harmonic response for a floating structure.…”

A 3D fully‐nonlinear potential‐flow solver for efficient simulations of large‐scale free‐surface waves

“…Towards boundaries, where it was shown by Ducrozet et al 23 that SG filters may ultimately amplify rather than reduce noise and/or errors, the SG filter is replaced by the selective filters developed by Berland et al 24 It is noted that filtering towards the domain boundaries is of little practical importance here due to the use of relaxation zones, but it may be of importance in later applications where wave‐structure interactions are considered. As a future development, the filters proposed by Shao et al, 25 improving the SG filters' ability to avoid sawtooth instabilities, may be considered.…”

A semi‐implicit finite volume scheme for a simplified hydrostatic model for fluid‐structure interaction

“…It is important to notice that it is never necessary to compute the inverse A −1 , because the products A −1 𝜟Z 2 and A −1 G can be obtained solving the systems AB = 𝜟Z 2 and AC = G, using the Thomas algorithm for tridiagonal systems.…”

“…Bradford 1 proposed a model in which the structure is the void resulting from the vertical subdivision of the domain in two regions of water, and each region is discretized by a $$$ \sigma $$$‐coordinate transformation of the grid. In the context of potential‐flow theory, Shao et al 2 include a floating body using a higher‐order boundary element method, while Tong et al 3 implement an immersed boundary method combined with a harmonic polynomial cell method. Ferrari and Dumbser 4 developed a semi‐implicit finite volume scheme for the free‐surface equations written in a conservative form that treats the nonhydrostatic pressure exerted against a fixed rigid body; in particular they use the diffuse interface approach, in which for each cell along the vertical the volume is limited and subdivided in the liquid, solid and void phases, while the pressure is unbounded.…”