半隐式离散方法求解非静水压强假设下的三维自由面流动  

Semi-implicit finite difference method for non-hydrostatic 3D free surface flows

作　　者：金生[1] 王昆[1] 

机构地区：[1]大连理工大学海岸及近海工程国家重点实验室,辽宁大连116024

出　　处：《水利水运工程学报》2008年第3期15-21,共7页Hydro-Science and Engineering

摘　　要：利用半隐式有限差分方法对非静水压强假设下的三维自由面流动问题进行模拟与讨论.此算法所描述的流动模型在通常情况下比静水压强假设下的流动模型更加精确,特别是针对一些地形变化比较剧烈的高频短波问题.在任意尺度的非规则区域上,采用三维Navier-Stokes方程来描述自由面流动的控制方程.动量方程、连续方程、自由面水位演进方程均采用半隐式离散格式进行离散.并通过三维线性驻波验证算例和连接丹麦与瑞典的跨海工程(Φresund海域)潮流模拟的应用算例,说明该模型模拟三维自由面流动问题较静压假设下的三维浅水模型具有较大的优越性.A semi-implicit finite difference model for non-hydrostatic 3D free surface flows is analyzed and discussed. It is shown that the present algorithm is generally more accurate than recently developed models for quasi-hydrostatic flows. The governing equations are the free surface Navier-stokes equations,defined on a general, irregular domain of arbitrary scale. The momentum equations, the incompressibility condition and the equation for the free surface adopt a semi-implicit discretization scheme. The final standing wave exemple and the simulation trend for the cross-sea project in Danmark and Sweden （Фresund sea area） show that the non-hydrostatic 3D free surface flows are more advantageous than the quasi-hydrostatic flows for 3D shallow water model.

关 键 词：三维Navier—Stokes方程 自由面方程 半隐式 非静水压强 

分 类 号：TV131[水利工程—水力学及河流动力学]