Bathymetry reconstruction from experimental data using PDE-constrained optimisation

Journal
Computers & fluids  
Volume
278
Article Number
106321
Citation
Computers & Fluids 278: 106321 (2024)
Publisher DOI
10.1016/j.compfluid.2024.106321
Scopus ID
2-s2.0-85194586352
Peer Reviewed
true
Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.
Subjects
Bathymetry reconstruction
PDE-constrained optimisation
Shallow water equations
Wave flume experiment
DDC Class
550: Earth Sciences, Geology
620: Engineering
510: Mathematics
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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