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Combined time-stepping and Trefftz approach for nonlinear wave-structure interaction

Generally, two approaches have been used to study the nonlinear wave-structure interaction in the context of offshore engineering in recent years. One is based on the Stokes perturbation procedure in the frequency domain and has been applied to weak-nonlinear problems. The other is based on a full nonlinear solution to the resulting wave field by a time-stepping procedure with boundary conditions applied on the moving free and body surfaces. In the present work an alternative solution method for nonlinear wave-structure interaction problems is proposed. The method is based on the evolution equations for the free-surface elevation and the free-surface potential, which are solved by the time-stepping procedure. The field problem is solved at each time step by the perturbation method combined with Trefftz approach. The method is applied to the study of the evolution of three-dimensional waves generated by a vertical circular cylinder oscillating in water of constant depth.