Morphological modeling using a fully coupled, total variation diminishing upwind‐biased centered scheme
Morphological modeling using a fully coupled, total variation diminishing upwind‐biased centered scheme
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DOI：
10.1002/wrcr.20138
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发表时间：
2013-06
影响因子：
5.4
通讯作者：
Wei Li;H. J. Vriend;Zhengbing Wang;D. S. Maren
中科院分区：
文献类型：
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作者：
Wei Li;H. J. Vriend;Zhengbing Wang;D. S. Maren
迄今为止，对具有复杂、快速变化流量的河流过程的高分辨率形态建模一直受到模型精度或计算效率的限制。最广泛使用的数值算法之一是基于总变差递减法，通过逆风法或中心法求解。逆风方案可保持高精度，但复杂且计算要求高，而中心方法的简单性和效率会损害精度。本文将最近开发的逆风中心方案扩展为刚性河床上的清水和标量输送，扩展到易蚀河床上的沉积物流动。它通过使用结构化网格的有限体积方法开发完全耦合的二维数学模型来实现这一点。一次性求解一整套非基于能力的控制方程，涉及床层变形和沉积物密度变化的影响，以及湍流和沉积物扩散的影响，以及沉积物适应所需的时间和空间尺度，以获得整个计算域的同步解。为了稳定性，源项采用两阶段分裂方法和二阶龙格库塔方法。该模型在涵盖各种复杂（含沉积物）流的大量测试中得到了验证。该模型被证明可以准确模拟冲击波和反射波，而且可以模拟高沉积物输送速率下的快速河床变形。高数值精度和计算效率的结合使该模型成为预测形态复杂地区洪水事件的重要工具。
High‐resolution morphological modeling of fluvial processes with complex, rapidly varying flows has been limited so far by model accuracy or computational efficiency. One of the most widely used numerical algorithms is based on the total variation diminishing method, solved by either upwind or centered approaches. An upwind scheme preserves high accuracy but is complex and computationally demanding, whereas the simplicity and efficiency of a centered approach compromise the accuracy. The present paper extends a recent upwind‐biased centered scheme originally developed for clear water and scalar transport over a rigid bed, to sediment‐laden flows over an erodible bed. It does so by developing a fully coupled 2‐D mathematical model using a finite volume method for structured grids. The complete set of noncapacity‐based governing equations, involving the effects of bed deformation and sediment density variation, as well as the influences of turbulence and sediment diffusion, and the temporal and spatial scales needed for sediment adaptation, is solved at one time to obtain synchronous solutions for the entire computational domain. For stability, a two‐stage splitting approach together with a second‐order Runge‐Kutta method is employed for the source terms. The model is verified in a number of tests covering a wide range of complex (sediment‐laden) flows. The model is demonstrated to accurately simulate shock waves and reflection waves, but also rapid bed deformations at high sediment transport rates. The combination of high numerical accuracy and computational efficiency makes the model an important tool to forecast flood events in morphologically complex areas.