高阶非线性Boussinesq型方程及其数值验证  

A set of high order nonlinear Boussinesq-type equations and its numerical verification

作　　者：张洪生[1] 周华伟[1] 洪广文[2] 

机构地区：[1]上海交通大学海洋工程国家重点实验室,上海200240 [2]河海大学港口海岸与近海工程学院,南京210024

出　　处：《水动力学研究与进展（A辑）》2011年第3期265-277,共13页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金资助项目(51079082;40676053);上海交通大学海洋工程国家重点实验室资助项目(GKZD010012;GP010818);华东师范大学河口海岸学国家重点实验室资助项目(200907)

摘　　要：从Laplace方程和非线性的边界条件出发,通过将波动速度势函数表达为任意特定水深处的函数,推导了线性频散关系具有Airy波精确解的Padé[2,2]阶近似精度的高阶非线性的Boussinesq型方程。方程含有能量耗散项并完全满足水底边界条件。定性比较了高阶非线性方程和弱非线性方程的非线性特征。推导了二维四阶的滤波公式。建立了非线性波传播的数值模拟模型。结合两个具体算例,比较了数值模拟模型的强非线性版本和弱非线性版本的计算结果之间的差别,从而定量探讨了高阶非线性项对数值计算结果的影响。With the wave velocity potential function being expressed as a function defined at an arbitrary water level, a set of high-order nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived set of equations is accurate up to [2, 2] pad6 approximation in linear dispersion, includes the dissipative terms and fully satisfies the sea bottom boundary condition. The nonlinear characteristic is compared between the present high order nonlinear equations and the weakly nonlinear ones. The two-dimension fourth order filter formula is also provided in this paper.The numerical model for wave propagation is described. With two test cases numerically high order nonlinear version of the numerical model are compared to those of the weakly the effects of high order nonlinear terms on wave propagation are studied quantitatively. simulated, the modeled results of the nonlinear version. This indicates that

关 键 词：BOUSSINESQ型方程 高阶非线性 弱非线性 数值模拟 

分 类 号：P731.2[天文地球—海洋科学] TV139.2[水利工程—水力学及河流动力学]