A semi-analytical computation of the three dimensional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with flat triangular elements. As a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference

The purpose of this work is twofold: to present a computational strategy to simulate the dynamics of a rigid sphere during water sloshing and to validate the model with original experimental data. The numerical solution is obtained through the coupling between a two-fluid Navier-Stokes solver and a rigid solid dynamics solver, based on a Newton scheme. A settling sphere case reported in the literature is first analyzed to validate the numerical strategy by ascertaining the settling velocity. In addition, an experiment is carried out based on a sphere submerged into a communicating vessel subjected to sloshing. Experimental data are captured using image processing and statistically treated to provide sphere dynamics quantitative information. The effects of different classical models used to describe drag coefficients, added mass, and wall effects are considered in the study to evaluate their influence on the results. The numerical model provides results that are consistent with the physical data, and the trajectory analysis shows good agreement between the simulations and the experiments.