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Hajduk, Hennes ; Kuzmin, Dmitri ; Aizinger, Vadym:
Bathymetry Reconstruction Using Inverse ShallowWater Models : Finite Element Discretization and Regularization.
In: van Brummelen, Harald ; Corsini, Alessandro ; Perotto, Simona ; Rozza, Gianluigi
(Hrsg.):
Numerical Methods for Flows : FEF 2017 Selected Contributions. -
Cham
: Springer
,
2020
. - S. 223-230
ISBN 978-3-030-30705-9
DOI: https://doi.org/10.1007/978-3-030-30705-9_20
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.