A direct solution approach to the inverse shallow-water problem
type: Item
instance of: scholarly article
title: A direct solution approach to the inverse shallow-water problem
zbMATH Open document ID: 1264.76033
DOI: 10.1155/2012/417950
author: Alelign Gessese
author: M. Sellier
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M32
zbMATH DE Number: 6173267
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/417950
OpenAlex ID: W2015691940
Wikidata QID: Q58911549
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description: scientific article; zbMATH DE number 6173267