Finite element simulations of second order wave resonance by motions of two bodies in a steady current

Wave resonance by forced motions of two bodies in a steady current is investigated in this paper. The work is based on second order theory of potential flow and the simulation is through a higher order finite element method with 12-node elements in time domain. Boundary conditions are imposed on mean positions of all boundaries. The i-th (i = 1,2) order potentials in the fluid domain at each time step are obtained by solving the finite element system and the spatial derivatives of the potential are calculated by differencing the shape functions directly. Numerical cases are given for two rectangular cylinders undergoing in specified oscillations in a steady current. The first and second order resonances have been captured at their resonant frequencies at different current speeds, which does not seem to have been studied yet. The numerical result shows that the current speed has important influence on the wave and force at both first and second order resonances. •A higher order finite element method has been employed to analyze wave-current-body interaction.•Both linear and resultant waves & forces have been affected by the current including amplitude, phase or nonlinearity.•Larger Froude number generally causes linear or second order wave and force to be smaller at its resonant frequency.•Second order wave and force increase as Froude number increases at in vertical motion and at in horizontal motion