An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations
An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations
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DOI：
10.1002/2016wr020055
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发表时间：
2017-05
影响因子：
5.4
通讯作者：
X. Xia;Q. Liang;X. Ming;J. Hou
中科院分区：
文献类型：
--
作者：
X. Xia;Q. Liang;X. Ming;J. Hou
求解完整二维浅水方程 (SWE) 的数值模型已越来越多地用于模拟地表水流，并更好地了解流域内山洪暴发的瞬态水流动力学。然而，全动态地表径流模型的开发仍然存在尚未解决的关键挑战，涉及（1）在消失水深限制下难以保持数值稳定性和准确性；（2）由于摩擦项的强非线性导致坡面速度和流量的估计不准确。本文旨在解决这些关键的研究挑战，并提出一种新的数值方案，用于准确有效地模拟复杂地形上的大规模瞬态地表水流。该方案采用新颖的表面重建方法（SRM）来正确计算坡度源项并在小水深下保持数值稳定性，并采用新的隐式离散化方法来处理高度非线性摩擦项。由此产生的浅水地表径流模型首先根据分析和实验测试案例进行验证，然后应用于模拟英国霍特惠斯尔伯恩 42 平方公里的假设降雨事件。
Numerical models solving the full 2‐D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large‐scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.