Fully Nonlinear Numerical Simulations of Wave Interactions with Multiple Structures at Resonance

A two-dimensional boundary element method (BEM) based on potential flow theory is adopted to study the wave interactions with multiple structures at resonance. Here resonance refers to the wave resonance which appears in the gaps between structures. The wave-structure interactions problems are simulated using a mixed Euler-Lagrangian scheme, with fully nonlinear boundary conditions applied on the instantaneous free surface and wetted body surface. The numerical scheme is verified through the simulations of wave interactions with a single body. Results show that both the free surface elevation and the hydrodynamic forces can be calculated accurately enough. The first primary study proposes a numerical approach to calculate the dominant natural frequencies in the gap based on the understanding of free liquid sloshing in a tank. The effectiveness of this approach is verified through the ‘response amplitude operator’ (RAO) analysis in terms of the gap free surface elevation. The natural frequencies are found for twin barges, with various gap widths and draughts. The effects of resonance on wave forces and elevations are also analysed. The second primary study considers the resonance induced by forced heave, sway and roll of body motion at various amplitudes. Particularly, second-order resonance, which is due to the sum or difference frequency, is found especially significant when the gap width over draught ratio is large. Second-order resonance can sometimes be as pronounced as, or even stronger than, classical first-order resonance. The third primary study concerns the wave resonance induced by nonlinear regular incident waves. For hydrodynamic interactions when the two bodies are both fixed, the free surface elevations are captured, particularly the standing wave trains formed in front of the upwave structure and sheltering effect behind the leeside structure. The nonlinearity associated with incident wave steepness is taken into consideration. Then second-order resonance in the gap caused by incident waves is studied. Finally, the wave resonance behaviour in the gap when the two bodies are freely floating under incident waves is analysed