Abstract
A three-dimensional numerical model based on the potential wave theory is developed for nonlinear irregular wave motion. The σ-transformation is employed to map the irregular and time-dependent domain of definition of the physical problem onto a strip of unit width so as to facilitate the implementation of the free surface and bottom boundary conditions. The finite difference method is used to solve the governing equations in the mapped coordinates. Non-reflective wave-generation is realized by combining virtual sources and a sponge layer. The numerical model is verified by the known solutions for nonlinear regular and irregular waves in water of constant depth. Standing waves in front of a vertical wall, runup of long waves on a sloping beach, and wave decomposition phenomenon over submerged bars are also studied. The model is also applied to a three-dimensional problem of nonlinear wave transformation over an elliptical shoal. The computational results are shown to agree well with the experimental data.
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