An enhanced numerical model for predicting higher-harmonic wave loads based on weak-scatterer theory

Accurate prediction of higher-harmonic wave loads is crucial for designing offshore structures to withstand extreme wave conditions. High-fidelity CFD and fully nonlinear potential-flow models are accurate but computationally expensive, whereas weak-scatterer (WS) theory offers an efficient alternative by strategically neglecting higher-order scatter wave effects while retaining fully nonlinear incident-wave kinematics. However, its application to steep and extreme waves has so far been limited, mainly due to numerical instabilities, and the validity of the underlying assumptions when higher-harmonic wave loads are of primary interest. This paper presents an enhanced numerical implementation of the WS theory that substantially extends its applicability, featuring (i) an effective nonlinear correction at the waterline, implemented as a post-processing step that recovers key nonlinear contributions neglected in the original WS formulation without adding complexity to the time-domain solver, and (ii) a tailored weighted least-squares low-pass filter that robustly stabilizes the time-domain simulations. Furthermore, (iii) a Morison-drag model based on the instantaneous Keulegan–Carpenter number is incorporated to estimate important viscous contributions for floating structures in extreme seas. We validate the enhanced numerical model and assess its performance in large-amplitude waves through benchmark cases, including monopiles and a semi-submersible floater. The results demonstrate stable and accurate simulations at high wave steepness, where comparable models may fail due to local wave breaking at the waterline, and confirm the critical role of the nonlinear waterline correction in reliably predicting higher-harmonic nonlinear wave loads for engineering applications.