A two‐dimensional vertical non‐hydrostatic σ model with an implicit method for free‐surface flows
A two‐dimensional vertical non‐hydrostatic σ model with an implicit method for free‐surface flows
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DOI：
10.1002/fld.670
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发表时间：
2004-03
影响因子：
1.8
通讯作者：
Hengliang Yuan;Chin H. Wu
中科院分区：
文献类型：
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作者：
Hengliang Yuan;Chin H. Wu
建立了σ坐标系下的隐式有限差分模型，用于求解非静力二维垂直面自由面流动。为了精确模拟自由表面流与不均匀底部的相互作用，采用全隐式方法分两步在正则变换σ域中同时求解非定常Navier-Stokes方程和自由表面边界条件。首先，将垂直速度和压力表示为水平速度的函数。其次，将这些关系代入水平动量方程，提供了一个以水平速度为未知数的块三对角矩阵系统，该系统可以通过直接矩阵求解器求解而无需迭代。开发了一种新的处理顶层单元的非静水压力条件，并发现其对于解决波传播的相位很重要。为了获得精确稳定的数值结果，对σ坐标变换引入的附加项进行了适当的离散化。所开发的模型已经通过几个试验进行了验证，这些试验涉及具有强垂直加速度的自由表面流和与不均匀底部相互作用的非线性波。数值结果、解析解和实验数据的比较表明了该模型模拟自由表面流动问题的能力。版权所有© 2004年约翰威利父子有限公司。
An implicit finite difference model in the σ co‐ordinate system is developed for non‐hydrostatic, two‐dimensional vertical plane free‐surface flows. To accurately simulate interaction of free‐surface flows with uneven bottoms, the unsteady Navier–Stokes equations and the free‐surface boundary condition are solved simultaneously in a regular transformed σ domain using a fully implicit method in two steps. First, the vertical velocity and pressure are expressed as functions of horizontal velocity. Second, substituting these relationship into the horizontal momentum equation provides a block tri‐diagonal matrix system with the unknown of horizontal velocity, which can be solved by a direct matrix solver without iteration. A new treatment of non‐hydrostatic pressure condition at the top‐layer cell is developed and found to be important for resolving the phase of wave propagation. Additional terms introduced by the σ co‐ordinate transformation are discretized appropriately in order to obtain accurate and stable numerical results. The developed model has been validated by several tests involving free‐surface flows with strong vertical accelerations and non‐linear waves interacting with uneven bottoms. Comparisons among numerical results, analytical solutions and experimental data show the capability of the model to simulate free‐surface flow problems. Copyright © 2004 John Wiley & Sons, Ltd.