Time-domain simulation of second-order irregular wave diffraction based on a hybrid water wave radiation condition

A time-domain second-order method is presented to simulate three-dimensional wave-body interaction. In the approach, Taylor series expansions are applied to the free surface boundary conditions, and a Stokes perturbation procedure is then used to establish the corresponding boundary value problem at first order and second order on the time-independent surfaces. A constant boundary element method, based on a Rankine source, is used to calculate the wave field at each time step. A proposed hybrid radiation condition, which is a combination of the multitransmitting formula and the damping zone, is studied to minimize the wave reflection, a stable integral form of the free-surface boundary condition is used to update the velocity potential on the free surface, and an auxiliary function is used to calculate high-order derivatives. The proposed model is first validated by linear irregular wave diffraction and is then applied to compute the second-order irregular Stokes wave diffraction with three wave components. It is shown that long time simulation can be performed with stability and accuracy and that the model can be used to simulate nonlinear irregular wave-structure interaction.