张俊生，滕 斌，丛培文

(大连理工大学 海岸和近海工程国家重点实验室，辽宁 大连 116024)

浅水中浮体在波浪作用下运动的三维时域计算模型

张俊生，滕 斌，丛培文

(大连理工大学 海岸和近海工程国家重点实验室，辽宁 大连 116024)

港口中系泊船在波浪作用下运动问题的本质是浅水波浪与浮体的相互作用。与深水情况不同，浅水问题应当考虑水底、水域边界的影响及浅水波浪自身的特性，单一模型很难实现该模拟过程。为此，建立了Boussinesq方程计算入射波和Laplace方程计算散射波的全时域组合计算模型。有限元法求解的Boussinesq方程能使入射波充分考虑到水底、水域边界的影响和浅水波浪的特性；散射波被线性化，采用边界元法求解，并以浮体运动时的物面条件为入射波和散射波求解的匹配条件。该方法为完全的时域方法，计算网格不随时间变动，计算过程较为方便。通过与实验及其他数值方法的结果进行比较，验证了本模型对非线性波面、浮体的运动都有比较理想的计算结果，显示了本模型对非线性问题具有较好的计算能力。

浅水中浮体运动；非线性波浪作用；Boussinesq方程；Laplace方程；三维时域数值模型

Abstract:The calculation of the wave-induced motion of a moored ship in a harbor is essentially a problem of calculating the wave-induced motion of a floating body in shallow water.In this case,the influence of the sea bed and boundaries as well as waves must be considered,as it is different from the problem in deep water.It is difficult to solve the problem by using a single model.Therefore,a combination of an improved Boussinesq equation,to calculate incident waves,and the Laplace equation,to calculate scattered waves,is used to establish a numerical model.The Boussinesq equation solved by the finite element method can embody the characteristics in shallow water while simulating incident waves,and scattered waves are solved by the boundary element method under the linear approximation.The two parts are matched through the boundary condition on the surface of the floating body.The present model is a full time-domain one,but computational grids do not change with the time,which makes the calculation convenient.While calculating nonlinear wave elevations and the motion of the floating body induced by nonlinear waves,the comparison of present results with experimental data and results of other numerical methods shows a good agreement and proves the combined model feasible to deal with nonlinear problems.The model is worthy of being applied to calculate the motion of the moored ship in engineering.

Keywords:motion of the floating body in shallow water; action of nonlinear waves; Boussinesq equation; Laplace equation; 3D time-domain numerical model

计算港口内系泊船在波浪作用下的运动是一个传统而远未解决的问题。准确计算需要考虑多方面问题：波浪的非线性、港口边界和地形、浮体的运动响应、系泊系统等，整个计算是一个复杂的耦合系统。其中，核心问题就是浅水中波浪作用下浮体运动响应的计算。……