A time-dependent numerical model of the mild-slope equation

On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin's model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin's model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin's model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real - time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research and engineering applications about the wave propagation in a biggish area.