湖泊三维流场数值模拟及其在东湖的应用  

Three-dimensional lake hydrodynamic numerical modeling and its application to Lake Donghu

作　　者：黄牧涛[1] 田勇[1] 

机构地区：[1]华中科技大学水电与数字化工程学院,武汉430074

出　　处：《水动力学研究与进展（A辑）》2014年第1期114-124,共11页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金(51209098);水利部公益性行业科研专项项目(20100108);华中科技大学自主创新基金项目(2012TS017)~~

摘　　要：该文精细化模拟了湖泊流场的时空变化,建立了?坐标系下的湖泊三维水动力数值模型。该模型采用非结构三角形网格和垂向?坐标来剖分计算区域,空间上采用有限体积法离散三维水动力方程组,时间上采用模式分裂技术,外模求解中,采用修正的四阶龙格库塔格式求解二维垂向积分方程时变项,运用Osher格式计算跨边界法向通量,获得水深分布和垂向平均流速。求解三维内模动量方程时,模型采用显示与隐式相结合的方法求解三维水流运动方程组,获得三维流场细节。在数值模拟中全面引入三维GIS技术来辅助完成前处理、后处理与可视化任务,以提高建模效率和减低建模成本。并以武汉东湖为研究示范,对不同气候条件下湖泊的三维流场结构和变化规律进行了深入分析,验证了三维水动力数值求解方法的有效性。In order to precisely simulate the complicated water movement, circulation and mixture schema of lakes, based on the Navier-Stokes equations with the Boussinesq approximation, the 3D unstructured grid finite volume numerical model with sigma vertical coordinate for lake hydrodynamic is developed. The numerical computational domain consists of non-overlapping unstructured triangular grids, while irregular bathymetry is represented in the vertical plane with a sigma-stretched vertical coordinate. The spatial discretization schemes of 3D hydrodynamic equations are conducted by using finite volume method. The horizontal momentum equations and the continuity equation on unstructured triangular grids are approximated using anexternal-internal mode splitting method. The external mode solution is solved by using a modified fourth-order Runge-Kutta time-stepping scheme to calculate the two-dimensional surface elevation field and the depth averaged velocities, and applying the Osher＇s scheme to compute numerical flux across the boundary of triangular elements in horizontal direction. The model＇s intemal momentum equation solution is solved numerically using a simple combined explicit and implicit scheme to get precise 3D flow details. Furthermore, the GIS techniques are introduced to aid the pre-and pro data processing involved in the numerical modeling tasks. The 3D lake flow structure and movement of Lake Donghu under the different metrology conditions are taken as test cases to demonstrate the effectiveness of the 3D lake hydrodynamic numerical modeling.

关 键 词：湖泊 三维水动力 有限体积法 非结构网格 数值模拟 三维GIS 

分 类 号：TV131.2[水利工程—水力学及河流动力学]