A new model to solve long waves shoaling on a slope using rectangular grids

Abstract

The aim of this study is to develop a new scheme to solve long waves shoaling on a slope by following the scheme which has been developed using Finite Element Method and cubic spline function. To simplify the computation code and reduce the computation time, piecewise linear and delta function were used as shape and weight function in elements where shoreline is not included, respectively. This means that time integration at each node can be executed explicitly like Finite Difference Method. On the other hand, piecewise linear function was used as shape and weight function in the elements including shoreline. The verification was done by making comparison between theoretical solution derived by Carrier & Greenspan and computation results. They agreed well when the number of mesh over a slope is more than 25 that corresponds to the case when the wave length is twice as long as the slope length.