A Numerical Study of Linear Long Water Waves over Variable Topographies using a Conformal Mapping

M. V. Flamarion, R. Ribeiro-Jr


In this work we present a numerical study of surface water waves over  variable topographies for the linear Euler equations based on a conformal mapping and Fourier transform. We show that in the shallow-water limit the Jacobian of the conformal mapping brings all the topographic effects from the bottom to the free surface. Implementation of the numerical method is illustrated by a MATLAB program. The numerical results are validated by comparing  them with exact solutions when the bottom topography is flat, and with theoretical results for an uneven topography.


Water waves; Conformal mapping; Euler equations; MATLAB

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DOI: https://doi.org/10.5540/tcam.2022.023.04.00625

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Trends in Computational and Applied Mathematics

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