Bathymetry reconstruction based on the zero-inertia shallow water approximation
Bathymetry reconstruction based on the zero-inertia shallow water approximation
复制标题
基于零惯性浅水近似的水深重建
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Sellier
中科院分区：
文献类型：
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作者：
A. Gessese;Kabila Mawanzi Wa;M. Sellier
了解河床地形对于模拟明渠水流的流体动力学至关重要。事实上，基于浅水近似的流量模型需要有关河床地形的先验信息，以准确捕获天然河流、河口和洪泛区的流量特征。我们在这里提出一种数值技术，用于根据零惯性浅水近似成立的陡峭明渠流的给定自由表面高程数据重建河床地形。在这种情况下，通过忽略惯性项同时保留河床坡度和摩擦项的影响来修改浅水方程。我们在这项工作中表明，通过代数运算，我们可以将控制方程重新改写为单个一阶偏微分方程，该方程描述了从已知的自由表面高程数据中查找床层地形的反演问题。有趣的是，分析表明反问题不需要床面粗糙度的知识。通过考虑非定常修正的浅水方程，使用 MacCormack 的显式数值格式求解正演问题。然而，反问题是使用特征方法来解决的。逆问题和正问题的结果在两个不同的测试用例上成功地进行了相互测试。
The knowledge of the channel bed topography is paramount in modeling the hydrodynamics of open channel flows. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features in natural rivers, estuaries, and flood plains. We present here a numerical technique for reconstructing the channel bed topography from given free surface elevation data for steep open channel flows for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. We show in this work that by algebraic manipulation, we can recast the governing equations into a single first-order partial differential equation which describes the inverse problem which consists in finding the bed topography from known free surface elevation data. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other on two different test cases.