Nonlinear wave resonance by four bottom-mounted cylinders in a uniform current using a higher order finite element method

The fully nonlinear wave potential theory is employed to analyze interactions of water waves and a group or an array of vertical cylinders in a uniform current in three-dimensions (3D). The nonlinear free surface boundary conditions are satisfied on the transient position. The velocity potential at each time step are solved through a higher order finite element method (HOFEM) with hexahedral 20-node parametric elements and the velocity on the free surface are obtained by differentiating the shape functions directly. The radiation condition is imposed through a damping zone method. Wave resonance for four bottom mounted cylinders at near-trapping modes is simulated with considering current effect. Waves and hydrodynamic forces are obtained to show their resonant behaviors at different current speeds and different incident wave amplitudes. Comparisons are also made with those by previous study and the time-domain second order solutions and agreement and disagreement are discussed between them.