The Green-Naghdi (GN) equations are shallow-water wave equations which can be solved to predict the nonlinear and dispersive effects of water waves propagating in coastal waters. In this study, we formulate the Level I GN equations for variable bathymetry in 3-D, and numerically model the refraction-diffraction problem as an initial-boundary-value problem. A finite-difference model, in conjunction with elliptic grid-generation, is developed to solve the GN equations. Nonlinear wave propagation over a varying bathymetry is presented for solitary and cnoidal waves. A number of benchmark cases have been tested and compared with the available theoretical predictions. The results are presented and discussed to reveal the accuracy of the present model.

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