基于双层Boussinesq方程的三维波浪数值模型及其验证  

A three-dimensional wave numerical model based on the two-layer Boussinesq equation and its validation

作　　者：邹文峰[1] 王平[1,2] 刘忠波 房克照[1] 孙家文[2] 张宁川[1] ZOU Wenfeng;WANG Ping;LIU Zhongbo;FANG Kezhao;SUN Jiawen;ZHANG Ningchuan(Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China;State Environmental Protection Key Laboratory of Marine Ecosystem Restoration,National Marine Environmental Monitoring Center,Dalian 116023,China;College of Transportation Engineering,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连理工大学海岸及近海工程国家重点实验室,辽宁大连116024 [2]国家海洋环境监测中心国家环境保护海洋生态环境整治修复重点实验室,辽宁大连116023 [3]大连海事大学交通运输工程学院,辽宁大连116026

出　　处：《海洋工程》2022年第6期41-50,共10页The Ocean Engineering

基　　金：国家自然科学基金资助项目(52171247,51779022,52071057,51709054);国家重点研发计划专项项目(2019YFC1407705);海岸及近海工程重点实验室开放基金资助项目(LP2107)。

摘　　要：Liu等[1]给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。The two-layer Boussinesq water wave equation with the highest derivative of 2 given by Liu et al.[1]has better dispersion and nonlinearity,based on which,a 3D wave numerical model with finite difference method is established.The equations are spatially discretized on rectangular grids,and using higher order derivatives to approximate the time and space items in the equation.For time integration,a composite 4th-order Adams-Bashforth-Moulton predict-correction format is used.The regular wave propagation process is simulated under deep water conditions,and the calculated wave surface agrees well with the analytical results,which reflects that the numerical model can well portray the wave surface process and the velocity variation at the wave surface;the horizontal and vertical velocities distributed along the water depth can be obtained more accurately for kh=2π,which is consistent with the results of the theoretical analysis.Finally,the numerical model is used to calculate the propagation transformation of regular waves over the three-dimensional characteristic terrain,and the numerical results are in good agreement with the relevant experimental data.The higher order nonlinear term will have some effect on the numerical results of the wave;more higher harmonics will be generated as the wave nonlinearity is enhanced and the water depth is reduced.The two-layer Boussinesq model developed in this research has good simulation accuracy for the evolution of strong nonlinear waves.

关 键 词：波浪 三维数值模型 有限差分法 非线性 双层Boussinesq方程 

分 类 号：TV139.2[水利工程—水力学及河流动力学]