极射赤面投影坐标系二维间断有限元水动力模型  

Two-Dimensional Hydrodynamic Model in Stereographic Projection Coordinate Systems Based on Discontinuous Galerkin Method

作　　者：张庆河[1] 王容基 李文俊 冉国全 Zhang Qinghe;Wang Rongji;Li Wenjun;Ran Guoquan(State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin 300072,China;CCCC Third Harbor Consultants Co.,Ltd.,Shanghai 200032,China)

机构地区：[1]天津大学水利工程仿真与安全国家重点实验室,天津300072 [2]中交第三航务工程勘察设计院有限公司,上海200032

出　　处：《天津大学学报（自然科学与工程技术版）》2021年第3期221-227,共7页Journal of Tianjin University：Science and Technology

基　　金：国家重点研发计划资助项目(2017YFC1404200);国家自然科学基金资助项目(U1906231).

摘　　要：针对普通经纬球坐标下二维浅水方程数值模型存在奇异点和网格辐合的问题,通过极射赤面投影方法将经纬球坐标转化为平面坐标实现网格重划,并应用无积分节点间断有限元空间离散方法,建立了可应用于大范围海域模拟的二维水动力数值模型.利用建立的模型模拟了渤海海域潮波和渤海湾局部潮流运动,模拟结果与实测数据吻合良好,表明极射赤面投影坐标下的二维间断有限元水动力模型能较好地模拟大范围海域潮波传播和局部海域潮流运动.To overcome the problems of coordinate singularity and grids convergence at the poles in numerical model of two-dimensional shallow water equations in the longitude-latitude spherical coordinate system,the stereographic projection method is applied to transform the spherical coordinates into plane coordinates and remesh the grids,and the quadrature-free nodal discontinuous Galerkin method is used to establish a two-dimensional hydrodynamic model that can be applied to large-scale sea area simulation.The model is used to simulate the tidal wave propagation in the Bohai Sea and the tidal flow in a local area in the Bohai Bay.The simulated results are well consistent with measured data.It is shown that the two-dimensional discontinuous Galerkin hydrodynamic model by using the sterographical projection method can well simulate the tidal wave propagation in a large area and the tidal flow in a local area.

关 键 词：极射赤面投影 无积分节点间断有限元 二维水动力模型 渤海 

分 类 号：TV131.4[水利工程—水力学及河流动力学] P731.2[天文地球—海洋科学]