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A Direct Solution Approach to the Inverse Shallow-Water Problem

机译：浅水反问题的直接求解方法

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摘要

The study of open channel flow modelling often requires an accurate representation of the channel bed topography to accurately predict the flow hydrodynamics. Experimental techniques are the most widely used approaches to measure the bed topographic elevation of open channels. However, they are usually cost and time consuming. Free surface measurement is, on the other hand, relatively easy to obtain using airborne photographic techniques. We present in this work an easy to implement and fast to solve numerical technique to identify the underlying bedrock topography from given free surface elevation data in shallow open channel flows. The main underlying idea is to derive explicit partial differential equations which govern this inverse reconstruction problem. The technique described here is a "one-shot technique" in the sense that the solution of the partial differential equation provides the solution to the inverse problem directly. The idea is tested on a set of artificial data obtained by first solving the forward problem governed by the shallow-water equations. Numerical results show that the channel bed topographic elevation can be reconstructed with a level of accuracy less than 3%. The method is also shown to be robust when noise is present in the input data.
机译：明渠水流建模的研究通常需要准确表示河床床面地形，以准确预测水流动力。实验技术是用于测量明渠河床地形高程的最广泛使用的方法。但是，它们通常是成本和时间消耗。另一方面，使用航空摄影技术比较容易获得自由表面测量值。我们在这项工作中提出了一种易于实现和快速解决的数值技术，该技术可以根据浅露天通道中给定的自由表面高程数据确定潜在的基岩地形。主要的基本思想是得出明确的偏微分方程，该方程控制该逆重构问题。从偏微分方程的解直接提供反问题的解的意义上来说，此处描述的技术是“一次性”技术。这个想法在一组人工数据上得到了检验，这些数据是首先解决由浅水方程控制的正向问题。数值结果表明，通道床地形高程的重建精度可低于3％。当输入数据中存在噪声时，该方法也显示出鲁棒性。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第10期|417950.1-417950.18|共18页
  • 作者

    Alelign Gessese; Mathieu Sellier;

  • 作者单位

    Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand,School of Mechanical and Industrial Engineering, Bahir Dar University, P.O. Box 26, Bahir Dar, Ethiopia;

    Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand;

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