An implicit two‐dimensional non‐hydrostatic model for free‐surface flows
An implicit two‐dimensional non‐hydrostatic model for free‐surface flows
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DOI：
10.1002/fld.1414
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发表时间：
2007-07
影响因子：
1.8
通讯作者：
A. Ahmadi;P. Badiei;M. Namin
中科院分区：
文献类型：
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作者：
A. Ahmadi;P. Badiei;M. Namin
在Sigma坐标系下建立了一种隐式有限体积模型来模拟二维垂直自由表面流动，采用非静力压力分布。该算法基于投影法，分两步求解完整的二维N-S方程。首先，剔除动量方程中的压力项，求解得到的对流扩散方程。第二步，求解只含压力项的连续性和动量方程，得到一个以压力为未知量的块三对角方程组。该方程组可用直接矩阵求解器求解，无需迭代。在顶层采用了类似于下层的非静水压力隐式处理，使模型在整个水柱中摆脱了任何静水压力假设。这种处理使模型能够更准确地评估自由面高程和波速。进行了一系列数值试验，包括具有显著垂直加速度的自由面流动和浅水区的非线性行为。将数值结果、解析解和实验数据进行了比较，结果令人满意。版权所有©2006 John Wiley&Sons，Ltd.
An implicit finite volume model in sigma coordinate system is developed to simulate two‐dimensional (2D) vertical free surface flows, deploying a non‐hydrostatic pressure distribution. The algorithm is based on a projection method which solves the complete 2D Navier–Stokes equations in two steps. First the pressure term in the momentum equations is excluded and the resultant advection–diffusion equations are solved. In the second step the continuity and the momentum equation with only the pressure terms are solved to give a block tri‐diagonal system of equation with pressure as the unknown. This system can be solved by a direct matrix solver without iteration. A new implicit treatment of non‐hydrostatic pressure, similar to the lower layers is applied to the top layer which makes the model free of any hydrostatic pressure assumption all through the water column. This treatment enables the model to evaluate both free surface elevation and wave celerity more accurately. A series of numerical tests including free‐surface flows with significant vertical accelerations and nonlinear behaviour in shoaling zone are performed. Comparison between numerical results, analytical solutions and experimental data demonstrates a satisfactory performance. Copyright © 2006 John Wiley & Sons, Ltd.