Extended linear refraction-diffraction model

An alternative derivation of the extended refraction-diffraction equation is presented. The bottom curvature and slope-squared terms ignored in the mild-slope equation are included to account for relatively steep and rapidly undulating bathymetry. The linear elliptic partial differential equation is solved by the hybrid element method and applied to three-dimensional bedforms. Quadratic triangular elements are used in the model so that the curvature can be calculated directly from the water depth defined at the nodes. The model is illustrated by simulating wave reflection from a ripple bed and wave transformation over a circular shoal in which previous experimental and numerical results exist. The relative effects of the additional terms and their significance in the model prediction are examined in a numerical experiment.