交错网格下四阶Boussinesq方程对潜堤上波浪演化的应用*

基于Madsen 和 Sch?ffer推导的四阶Boussinesq方程，在交错网格下建立一维数值模型。模型中的时间导数采用混合四阶Adams-Bashforth-Moulton 格式。为了避免二次反射，采用了Gobbi 和 Kirby的的内部源函数造波法。最后数值模拟了波浪在潜堤上的演化过程，并且与Luth的试验值进行对比，结果显示两者吻合较好，另外还给出了非交错网格下的模拟结果，通过对比可知，两个模型都能够很好地模拟波浪在潜堤上的演化过程。

Application of a fourth-order Boussinesq model in staggered grids for wave evolution over a submerged sill

Based on a fourth-order Boussinesq model by Madsen and Sch?ffer,a numerical implementation of the model in one horizontal direction is established by finite difference method in staggered grids.A composite forth order Adams-Bashforth-Moulton scheme is used to step the model forward in time.A grid-interior source function presented by Gobbi and Kirby is utilized in present model to avoid the re-refraction.Numerical simulations of wave propagating over a submerged sill are carried out.And the Luth et al’s(1994) laboratory data are used to test the applicability of the present model,and the numerical results are in general agreement with laboratory data.In addition,numerical results based on the Boussinesq model in non-staggered grids are given.Results show that both models can well simulate the wave evolution over a submerged sill.