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12A finite element method for the solution of the up-to-second-order wave diffraction-radiation 13 problem in the time-domain is proposed. The solver has been verified against available analytical 14 solutions, and validated against experimental data available for the HiPRWind semisubmersible platform 15 (designed for floating wind turbines). To perform the validation, the wave diffraction-radiation solver is 16 coupled to a body dynamics and mooring solvers in the time-domain. The HiPRWind movements and 17 mooring forces have been compared for a large number of test cases, including decay tests, 18 monochromatic waves, bichromatic and irregular waves. Good agreement has been found for both, body 19 movements and mooring forces. 20

The application of the semi-Lagrangian Particle Finite Element Method (SL-PFEM) for the seakeeping simulation of the Wave Adaptive Modular Vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented. Keywords Particle Finite Element Method • semi-Lagrangian formulations • seakeeping 1 Introduction The Particle Finite Element Method (PFEM) [18] is a versatile framework for the analysis of fluid-structure interaction problems. The PFEM combines Lagrangian particle-based techniques with the advantage of the integral formulation of the Finite Element Method (FEM). It has been shown [14, 15,21, 28, 13, 27] to successfully simulate a wide variety of complex engineering problems, e.g., free-surface/multi-fluid flows with violent interface motions, multi-fluid mixing and