一维全非线性Green-Naghdi水波方程数值模型  

A numerical scheme for one-dimensional and fully nonlinear Green-Naghdi wave equations

作　　者：焦子峰 尹晶[1,2] 房克照[1] 孙家文[1,2] JIAO Zifeng YIN Jing FANG Kezhao SUN Jiawen(The State Key Laboratory of Coastal and Offshore Engineering, Ocean Engineering Joint Research Center of DUT-UWA, Dalian University of Technology, Dalian 116024, China National Marine Environmental Monitoring Center, State Oceanic Administration, Dalian 116023, China)

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室DUT-UWA海洋工程联合研究中心,辽宁大连116024 [2]国家海洋环境监测中心,辽宁大连116023

出　　处：《海洋工程》2016年第6期30-37,共8页The Ocean Engineering

基　　金：国家自然科学基金资助项目(51579034);中国科学院海洋环流与波动重点实验室开放基金课题资助(KLOCW1502);辽宁省教育厅重点实验室基础研究项目资助(LZ2015013)

摘　　要：建立了求解一维全非线性Green-Naghdi水波方程的中心有限体积/有限差分混合数值格式。采用结构化网格对守恒形式的控制方程进行离散和积分,界面数值通量采用有限体积法计算,剩余项则采用中心有限差分格式求解。其中,采用中心迎风有限体积格式计算控制体界面数值通量,并结合界面变量的线性重构方法,使其在空间上具有四阶精度,通过引入静压重构技术和波浪破碎指标使模型具备处理海岸水-陆动边界及波浪破碎的能力。时间积分则采用具有总时间变差减小(Total Variation Diminishing,TVD)性质的三阶龙格-库塔法进行。应用该模型对孤立波在常水深和斜坡海岸上的传播过程及规则波跨越潜堤传播的实验进行了数值模型研究,数值计算同解析解及实验数据吻合良好。A 1D Green-Naghdi model based on hybrid central finite-volume / finite-difference method is presented in this paper. The convective flux in the conservative governing equations is estimated using finite- volume method while the remaining terms are discretized using finite-difference method. Central upwind finite-volume scheme,in conjunction with fourth-order MUSCL method for variables reconstruction,is used to compute the interface flux. By introducing the hydrostatic reconstruction technique and wave breaking index,the model has the ability to deal with the coastal moving shoreline and wave breaking. The third-order Runge-Kutta method with TVD property is adopted to perform time marching. The propagation of solitary wave on plane and sloping beach and the experiment of regular propagating over a submerged sill are computed with this model. The numerical results are in good agreement with analytical and experimental data.

关 键 词：Green-Naghdi水波方程 混合格式 中心迎风格式 水-陆动边界 波浪破碎 

分 类 号：O353.2[理学—流体力学]