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 bichromatic incident waves. The present model is considered as a complete second-order wave-load model, as all the second-order wave loads, including the sum-frequency and difference-frequency components, are solved simultaneously.

中文翻译：

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具有大水平运动的浮动结构时域一致的二阶水动力模型

浮式海上结构在水平面上往往表现出低频振荡运动，其振幅与其特征尺寸相同，且大于相应的波频响应，使得惯性坐标系中的传统公式不一致，适用性较差。为了解决这个问题，我们扩展和探索了一个完全基于非惯性体固定坐标系的替代公式。与传统的耐波模型不同，该公式始终允许大振幅水平运动。应用基于高阶边界元的数值模型来解决时域中的边界值问题。最近开发的一组新的显式时间积分方法，不需要对空间导数使用迎风方案，可用于处理对流型自由表面条件。为了抑制时间推进中自由表面上的弱锯齿不稳定性，我们还提出了基于优化加权最小二乘法的新型低通滤波器，其原则上适用于结构化和非结构化网格。所提出的对流方程和低通滤波器方案也适用于处理类似数学问题的其他工程领域。对于船舶耐波性和附加阻力分析，我们表明，与传统模型相比，目前的计算模型不需要使用软弹簧来进行冲击和摇摆。对于浮动单桩，考虑到双色入射波，证明了始终考虑大水平运动的影响的重要性。本模型被认为是一个完整的二阶波浪荷载模型，因为所有二阶波浪荷载，包括和频分量和差频分量，都是同时求解的。