The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this aim, a Smooth Particle Hydrodynamics (SPH) solver for simulating internal flows in tanks is coupled in the time domain to a Finite Element Method (FEM) diffraction-radiation solver developed for seakeeping problems. Validations are carried out comparing against available experimental data. Good agreement between obtained numerical results and experimental data is found.

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In this paper, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet algorithm, which uses an explicit integration for the particle's trajectory and an implicit integration for the velocity. The algorithm is completed with a predictor-multicorrector scheme for the integration of the velocity correction using the Finite Element Method. A second order projector based on least squares is used to transfer the intrinsic variables information from the particles onto the background mesh, while a second order interpolation scheme is used to transfer the accelerations from the mesh to the particles. Convergence analyses are carried out to assess the second order convergence.