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

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.