摘要
统一方程是在Stokes波理论与Boussinesq型方程相结合的基础上推导出的,适用于深水及浅水域波浪的传播。文中首先分析了统一方程的频散性及其适用性。其次,采用ADI法对控制方程进行离散,并对控制方程中的非线性项进行线性化近似处理,用改进的Patankar半隐格式方法求解动量方程。直接给定入射边界条件,出流边界条件采用Sommerfeld边界条件和消波层相结合的方法,从而建立起从深水到浅水域都有效的数值模型。最后,利用平底与圆形暗礁组合地形上波浪传播的经典物理模型实验来验证数值模型的精确性。将实验结果与数值解相比较,两者吻合较好,说明本文建立的数学模型能有效地模拟水深复杂变化水域波浪传播,具有较高的适用性。
The unified equations are derived from the Stokes second-order wave theory and the Boussinesq-type equations.It is suitable for the propagation of waves in deep and shallow seas.We firstly analyzed the dispersion and applicability of the unified equations,then used the ADI method to disperse the governing equations,processed the nonlinear terms of the governing equations by linear approximation,and used the modified Patankar with semi-implicit schemes to solve the momentum equations.Given the boundary conditions,the outflow boundary conditions are combined with the Sommerfeld boundary condition and the wave elimination layer,so as to establish a valid numerical model suitable for wave transformation from deep water to shallow water.At last,the experiment data from physical model of wave propagation and deformation in the complicated water is used to verify the accuracy of present numerical model.The experimental results are in good agreement with those of numerical solution.It indicates that the numerical model can effectively simulate the wave propagation in the water with varying topography,and has a high applicability.
作者
张文海
贾会杰
王炎
ZHANG Wen-hai;JIA Hui-jie;WANG Yan(No. 1 Engineering Co., Ltd. of CCCC First Harbor Engineering Co., Ltd., Tianjin 300456, China)
出处
《中国港湾建设》
2017年第6期36-40,共5页
China Harbour Engineering
关键词
统一方程
数值模拟
消波
非线性波
物理模型实验
unified equations
numerical simulation
absorbing waves
nonlinear wave
physical experiment
