波浪在潜堤上破碎的数值分析

Numerical analysis of waves breaking on a submerged breakwater

为模拟潜堤上的波浪破碎,在高阶Boussinesq方程中引入二阶紊动粘性项,建立了考虑波浪破碎的Boussinesq数值模型。在非交错网格下利用预报—校正的有限差分法求解控制方程,其中预报采用了三阶Adams-Bashforth格式和校正采用四阶Adams-Moulton格式。利用数值模型,通过数值试验,再现了波浪在不同坡度的潜堤上破碎演变过程。首先通过一组地形,将计算波面的时间历程与实验结果进行了对比,讨论和分析了二阶紊动粘性项中启动破碎的参数对数值计算结果的影响,给出模拟该问题时最优参数取值,进而通过其他两组地形的数值计算结果验证参数取值的合理性。

In order to model the waves breaking on a submerged breakwater and consider energy dis- sipation on the basis of breaking property, a numerical model for breaking waves was given by adding second order eddy viscosity terms to the fourth order dispersive Boussinesq equations. The numerical model was established with the finite differential method in non-staggered grids, and the model was solved with the third-order Adams-Bashforth predictor and the fourth-order Adams-Moul- ton corrector. Numerical experiments were firstly carried out to obtain the optimum breaking parame- ter involved in the eddy viscosity term. Then, based on the optimum value, numerical simulations of waves breaking on a submerged breakwater with different back slope were performed. The computed surface elevations varying with time in different locations were compared to experimental data, and the agreement was reasonably satisfactory, which demonstrates the present method considering ener-gy dissipation in Boussinesq wave model is effective.