A robust 2D shallow water model for solving flow over complex topography using homogenous flux method
A robust 2D shallow water model for solving flow over complex topography using homogenous flux method
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DOI：
10.1002/fld.3795
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发表时间：
2013-09
影响因子：
1.8
通讯作者：
M. Guan;N. Wright;P. Sleigh
中科院分区：
文献类型：
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作者：
M. Guan;N. Wright;P. Sleigh
提出了一种求解二维SWEs的稳健Godunov型数值格式求解器，并将其应用于模拟复杂地形上的干湿两相流动。在实际中，地形通常是复杂和不规则的，因此，为了避免由这些特征产生的数值误差，在SWES中使用了均匀通量方法来处理河床坡度项。该方法将床面斜率项作为通量并入通量梯度，从而在Godunov型激波捕捉方案中保持两者之间的平衡。该方法的主要优点是：第一，方法简单，易于实现；第二，数值实验表明，它可以处理不连续或垂直的床面地形，不需要任何特殊处理；第三，它既适用于定常流动，也适用于非定常流动。通过算例说明了该方法是如何应用于非线性双曲型方程组的。然后利用加权平均通量法的二阶全变差递减形式和包含新通量梯度项的Harten-Lax-van Leer收缩近似Riemann求解器来求解二维双曲组。通过几个基准试验对模型进行了验证，并与欧盟溃坝协同行动模型项目的实验测量结果进行了对比验证。这些都显示出非常好的一致性。最后，将该方法应用于具有复杂不规则地形的初始干燥河道上的火山引发的洪水，以验证该方法对真实洪水的模拟能力。版权所有©2013 John Wiley&Sons，Ltd.
A robust Godunov‐type numerical scheme solver is proposed for solving 2D SWEs and is applied to simulate flow over complex topography with wetting and drying. In reality, the topography is usually complex and irregular; therefore, to avoid the numerical errors generated by such features, a Homogenous Flux Method is used to handle the bed slope term in the SWEs. The method treats the bed slope term as a flux to be incorporated into the flux gradient and so maintains the balance between the two in a Godunov‐type shock‐capturing scheme. The main advantages of the method are: first, it is simple and easy to implement; second, numerical experiments demonstrate that it can handle discontinuous or vertical bed topography without any special treatment and third, it is applicable to both steady and unsteady flows. It is demonstrated how the approach set out here can be applied to the nonlinear hyperbolic system of the SWEs. The two‐dimensional hyperbolic system is then solved by use of a second‐order total‐variation‐diminishing version of the weighted average flux method in conjunction with a Harten‐Lax‐van Leer‐Contract approximate Riemann solver incorporating the new flux gradient term. Several benchmark tests are presented to validate the model and the approach is verified against experimental measurements from the European Union Concerted Action on Dam Break Modelling project. These show very good agreement. Finally, the method is applied to a volcano‐induced outburst flood over an initially dry channel with complex irregular topography to demonstrate the technique's capability in simulating a real flood. Copyright © 2013 John Wiley & Sons, Ltd.