On Modelling the Scattering of Highly Nonlinear Transient Water Waves Due to Surface-Piercing Cylinder. Part I: Formulations and Verifications

The presence of extreme ocean waves poses substantial threats to the safety of marine engineering applications and navigational activities. Accurate prediction of the nonlinear wave loads on offshore structures in large-diameter cylindrical configuration, such as monopile wind turbines and platform columns, requires a robust solution to the high-order wave diffraction problem. This paper introduces a novel, highly nonlinear time-domain numerical pseudo-spectrum model based on potential flow theory. By leveraging the Fredholm integral equation of the second kind and Legendre polynomials, a distinct efficient solver for computing the velocity potential on the cylinder surface and vertical velocity at free surface is developed. The present method is verified by comparing with a direct approach based on Fourier transform and established theoretical models for simulating the scattering of small steepness uniform waves. The convergence and computational efficiency of the present method is also demonstrated. The validation of the new model for simulating highly nonlinear transient water waves will be reported in Part II. The proposed model provides a powerful and efficient new framework for analyzing high-order nonlinear wave diffraction and hydrodynamic loads, with significant implications for both scientific research and the engineering design of coastal and offshore structures.