文章摘要
胡德超,张红武,钟德钰.C-D无结构网格上的三维自由水面非静水压力流动模型Ⅰ：算法[J].水利学报,2009,40(8):
C-D无结构网格上的三维自由水面非静水压力流动模型Ⅰ：算法
Three dimensional non hydrostatic pressure model for free surface flowson C-D unstructured grid Ⅰ. Scheme
  
DOI：
中文关键词: 三维  数学模型  C-D网格  无结构网格  自由流动  非静水
英文关键词: 3-D  numerical model  C-D grid  unstructured grid  free surface flow  non hydrostatic
基金项目:
作者单位
胡德超 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 
张红武  
钟德钰  
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中文摘要:
      为准确模拟垂向运动尺度较大的水流运动，本文基于压力分裂模式和半隐方法提出了C-D无结构、z坐标网格上的三维非静水压力流动模型的构造方法，并详细论述了模型的求解过程。模型先在忽略动水压强项的隐式部分的条件下求解控制方程，获得比较接近的初始解；再考虑动水压强项的隐式部分并求解一个关于它的三维Poisson方程，因此计算容易收敛。本文模型与传统的C网格上的非静水模型相比，增加了对水平切向动量方程的求解，消除了因C网格的简化处理所带来的精度损失。控制方程用有限体积-有限差分法离散，自由水面用水位函数法处理。对水位η和动水压强q分别采用不同的隐式因子以兼顾各自稳定和精度的要求。压力分裂模式、θ半隐方法和欧拉-拉格朗日方法(ELM)等的联合使用使得本模型具有简单、稳定、高效的特点。
英文摘要:
      In order to accurately simulate the free surface flows which have notable vertical motion, based on the pressure splitting and semi implicit method, a formulation of the 3-D non hydrostatic pressure model on C-D unstructured, z level grid is proposed and its numerical scheme is detailed. For accelerating the convergence of computation, the equations are solved at two steps by decomposing the pressure into hydrostatic and non hydrostatic parts. Firstly, an approximate solution is obtained by solving the momentum equations without the implicit part of the hydrodynamic pressure term. Secondly, the approximate solution is corrected by solving the 3 D Poisson equations involving the implicit part of the hydrodynamic pressures. Comparing with the models on the traditional C grid, this model involves the tangential momentum equation and avoids the errors caused by the simplicities of the C grid. The governing equations are discretized by a finite difference finite volume algorithm, and the free surface of flow is described by water level function method. Considering the requirement of the numerical stability and exactness, different semi implicit factors are used for calculating the free surface and hydrodynamic pressure. The combination of the pressure splitting method, θ semi implicit method and Eulerian Lagrangian Method make this model simple, stable and efficient.
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