非线性波浪时域计算的三维耦合模型

A three-dimensional coupled model for time-domain calculation of nonlinear waves

将计算区域Ω划分为内域Ω1和外域Ω２（Ω２＝Ω－Ω１），外域控制方程采用改进线性频散特性的二维Ｂｏｕｓｓｉｎｅｓｑ方程，用预报一校正法数值求解；结构物附近的内域控制方程为三维Ｎａｖｉｅｒ—Ｓｔｏｋｅｓ方程，由ＶＯＦ方法数值求解．通过在外域和内域相匹配的交界面上设置合适的速度和波面边界条件，建立了三维非线性波浪时域计算的耦合模型．模拟试验表明：（１）耦合模型数值波浪水池可以产生稳定的、重复性较好的波动过程；（２）用耦合模型数值波浪水池求解较大浅水区域上的非线性波浪数值计算问题可以取得较高的计算效率，同时又能得出结构物附近的复杂流场。

The coupled model, which is the combination of Boussinesq equations and the general description for three-dimensional (3-D) flows with the volume of fluid (VOF) method, has been developed for the numerical simulations of nonlinear waves in a large domain. That is, the whole computational domain Ω is divided into two sub- regions. In the near-field around a structure, Ω1, the flow is governed by 3-D Navier -Stokes equations and numerically solved by the VOF method. Whereas in the sub-region Ω2(Ω2 =Ω -Ω1), the flow is governed by two- dimensional Boussinesq equations and numerically solved with the predictor - corrector algorithm. The velocity and the wave surface elevation are matched to the common boundaries of the two sub-regions. Numerical verifications have been conducted for the case of wave propagation and interaction with a square caisson. It is shown that the coupled model is effective on computing nonlinear waves in a lame domain with taking into account the complicated flow field near a structure.