Wave diffraction in a current over a local shoal

Applying the Green's theorem and a moving oscillating source as the Green's function, an integral equation method is developed for predicting wave height over a shoal in a weak current. The integral equation is discretized by a higher order element method and a numerical code is implemented. To validate the numerical code, comparison is made on wave run-up around a vertical cylinder with McCamy and Fuchs' analytic solution in the still water and the results in currents from numerical wave tanks. Computation has also been carried out for the wave diffraction over a parabolic shoal in a current, and numerical results are given at many sections. The numerical results from the calculation can be used for benchmark test for other methods on wave diffraction in current.