Numerical simulations of non-linear wave radiation in inviscid fluid with a free surface

The paper deals with the numerical simulation of non-linear wave radiation by vertical free-surface piercing structures moving horizontally in water of finite constant depth. A time-stepping approach combined with the finite element method is used to simulate the potential flows due to high-frequency oscillations of the structure. The evolution equations for the wave elevation and velocity potential at the free surface, exact up to second order, are derived using Stokes perturbation expansion. The boundary value problems up to second order at each time-step are solved using the Eulerian description and a fixed mesh of finite elements. The results of simulations are presented for vertical cylinders of circular cross section, and for sloshing waves in annular tanks.