四阶Boussinesq模型验证及非线性精度对数值结果的影响

Validation of a Fourth Order Boussinesq Model and the Effect of Nonlinearity Accuracy on Numerical Results

基于Madsen和Schffer(1998)给出的一组四阶Boussinesq模型,在非交错网格下基于有限差分法建立了一维数值求解模型。在时间步进上采用三阶Adams-Bashforth预报、四阶Adams-Moulton校正的格式,模型中引入了内部源项,这更有效地避免造波板二次反射问题。数值模拟了波浪在潜堤上的波浪传播变形,利用Luth等(1994)的实验数据来检验本文模型。在模拟Ohyama等(1994)的实验时,讨论非线性精度对数值结果的影响,结果表明高阶非线性对数值模拟波浪演变非常重要:非线性精度越高,其对比效果越好。

Based on a fourth order Boussinesq model by Madsen and Schǎffer （ 1998 ）, a numerical implementation of the model in one horizontal direction is established by finite difference method in unstaggered grids. A composite fourth order Adams-Bashforth-Moulton scheme is used to step the model forward in time. A grid-interior source function is utilized in present model to avoid the re-reflection. Numerical simulations of wave propagating over submerged sills are carded out. Experimental data by Luth et. al （1994） are used to test the applicability of the present model. Numerical simulations are done upon the Ohyama el.al＇s experiment （1994）, and the effects of three different nonlinearities in present model are discussed. Results demonstrate high order nonlinearity is important in Boussinesq modelling of wave evolution： The higher the nonlinear accuracy is, the better the comparison is.