【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。更多还原

【Abstract】 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 pressuresplitting method,θ semi-implicit method and Eulerian-Lagrangian Method make this model simple,stable and efficient.更多还原