Combined refraction-diffraction wave model based on extended mild-slope equation

A numerical model for wave propagating and deforming over an uneven bottom with arbitrary boundaries is presented. An extended form of the time-depended mild-slope equation is employed as the control equation, in which the terms of (del(h)h)(2) and del(h)(2) h, bottom h friction, wind energy input and nonlinear dispersion are involved. For the convenience of numerical solution, the equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is used to solve it. The numerical method has the advantage of good stability and high efficiency. Several tests are carried out on the effects of bottom friction and wind energy input. The results show that the numerical method is sufficiently accurate as compared to analytic solution and that the effects of bottom friction and wind energy input are significant on some circumstances.