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Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling

机译:提高二维洪水模拟浅水方程简单公式的稳定性

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摘要

The ability of two-dimensional hydrodynamic models to accurately and efficiently predict the propagation of floods over large urban areas is of paramount importance for flood risk assessment and management. Paradoxically, it is in these highly relevant urban domains where flood modeling faces some of the most challenging obstacles. This is because of the very high-resolution topography that is typically required to capture key hydraulic features, which significantly increases the computational time of the model. One particularly interesting solution to this difficulty was recently proposed in the form of a numerical scheme for the solution of a simplified version of the shallow water equations, which yields a system of two explicit equations that captures the most relevant hydraulic processes at very high computational efficiency. However, some stability problems were reported, especially when this formulation is applied to low friction areas. This is of particular importance in urban areas, where smooth surfaces are usually abundant. This paper proposes and tests two modifications of this previous numerical scheme that considerably improves the numerical stability of the model. Model improvements were assessed against a structured set of idealized test cases and finally in the simulation of flood propagation over complex topography in a highly urbanized area in London, United Kingdom. The enhanced stability achieved by the new formulation comes at no significant additional computational cost and, in fact, the model performance can benefit from the longer time steps that are allowed by the new scheme.
机译:二维流体动力学模型能够准确有效地预测大城市地区洪水的扩散能力,对于洪水风险评估和管理至关重要。矛盾的是,在这些高度相关的城市领域中,洪水建模面临一些最具挑战性的障碍。这是因为捕获关键水力特征通常需要非常高分辨率的地形,这大大增加了模型的计算时间。最近以数值方案的形式提出了一种特别有趣的解决方案,用于简化形式的浅水方程组的求解,该方案产生了两个显式方程组,该系统以非常高的计算效率捕获了最相关的水力过程。 。但是,报告了一些稳定性问题,尤其是当该配方应用于低摩擦区域时。这在通常有大量光滑表面的城市地区尤为重要。本文提出并测试了此先前数值方案的两个修改,这些修改大大改善了模型的数值稳定性。模型改进是根据一组结构化的理想测试用例进行评估的,最后评估了英国伦敦高度城市化地区复杂地形上的洪水传播。通过新公式实现的增强的稳定性不会增加任何额外的计算成本,实际上,模型性能可以受益于新方案所允许的更长的时间步长。

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