Authors: | Hajduk, Hennes Kuzmin, Dmitri Aizinger, Vadym |
Title: | Bathymetry reconstruction using inverse shallow water models: Finite element discretization and regularization |
Language (ISO): | en |
Abstract: | In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner. |
Subject Headings: | Bathymetry reconstruction shallow water equations continuous/ discontinuous Galerkin method inverse problem |
Subject Headings (RSWK): | Bathymetrie Galerkin-Methode |
URI: | http://hdl.handle.net/2003/36876 http://dx.doi.org/10.17877/DE290R-18875 |
Issue Date: | 2018-04 |
Appears in Collections: | Ergebnisberichte des Instituts für Angewandte Mathematik |
Files in This Item:
File | Description | Size | Format | |
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Ergebnisbericht Nr. 585.pdf | DNB | 1.3 MB | Adobe PDF | View/Open |
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