Second-Order Extension of Wave Refraction/Diffraction Solution Over Variable Bathymetry

In this study, we attempt to extend the existing second-order wave diffraction problem to the second-order wave refraction/diffraction problem over variable bathymetry. The entire fluid domain is subdivided into interior and exterior domains by placing a matching surface. The interior domain contains floating/submerged structures and variable seabed bathymetry while the seabed is assumed to be flat extending radially from matching surface to infinity. Since the explicit form of second-order incident wave potential does not exist for arbitrary seabed, we manipulated the boundary integral equation for the 2nd-order diffraction potential, and then it was applied to both flat and variable bathymetry problems. The proposed method has been validated against well-established 1st-order refraction/diffraction and 2nd-order diffraction numerical examples.