基于无结构、σ坐标网格的半隐式三维水沙数学模型Ⅰ-算法  

3-D hydrodynamic model for free-surface flows and sediment transport on unstructured σ-coordinate grid.Part I.Numerical scheme

作　　者：胡德超[1,2] 张红武[1] 哈岸英[3] 赵维阳 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [2]长江科学院河流研究所,武汉430010 [3]西安理工大学,西安710048 [4]长江航道规划设计研究院,武汉430011

出　　处：《水力发电学报》2011年第6期221-229,共9页Journal of Hydroelectric Engineering

基　　金：国家自然科学基金项目(51039003;51109009);国家重点基础研究发展计划(2007CB714100)

摘　　要：针对天然河流水域边界不规则的特点,提出了平面无结构、垂向σ坐标网格上三维自由水面水沙数学模型的基本框架。模型基于压力分裂模式和θ半隐算法建立,求解分为两步,第一步求解一个关于自由水面的二维Poisson方程,获得水位和临时流场;第二步求解一个关于动水压强的三维Poisson方程,获得动水压强场并用它来校正临时流速场。在构造动水压强三维Poisson方程时借鉴了BOM模型方法,而在自由水面处理上摒弃了其内外模分裂方法,因而模型不受模式分裂方法中一致性问题的影响。在三维水流模型的基础上建立了悬移质泥沙模型,采用欧拉-拉各朗日方法(ELM)求解控制方程中的对流项,使模型计算的时间步长不受CFL稳定条件限制。A formulation of 3-D hydrodynamic model is proposed for simulation of complex free-surface flows and sediment transport in natural rivers on unstructured,σ-coordinate grids.Two computation steps are adopted to solve the equations with a pressure-splitting and θ semi-implicit method.First,free surface and provisional velocity filed are obtained by solving a 2-D Poisson equation;second,non-hydrostatic pressures are computed by solving a 3-D Poisson equation and the provisional velocity filed is corrected.In constructing this 3-D Poisson equation,the methods of BOM model were adopted,while its mode-split technique was discarded to overcome the inconsistencies.In the sediment transport model that was developed on the hydrodynamic model,an Eulerian-Lagrangian Method（ELM） is used to solve the governing equations,so that the computation time steps are not restricted to the CFL stability conditions.

关 键 词：泥沙动力学 三维 数学模型 水流 泥沙 无结构网格 Σ坐标 自由水面 

分 类 号：TV143[水利工程—水力学及河流动力学]