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            <note type="commentary">73 pages,  15 figures, 1 table, 80 references. Published in Commun. Comput. Phys. In this version minor typos were corrected. Other author's papers can be downloaded at http://www.denys-dutykh.com/</note>
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                <term xml:lang="en">wave energy extraction</term>
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                <term xml:lang="en">wave damping</term>
                <term xml:lang="en">wave run-up</term>
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                <term xml:lang="en">movable wall</term>
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              <p>In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution is described with the free surface potential flow model. Then, a semi-analytical numerical method is presented. It is based on a mapping technique and a finite difference scheme in the transformed domain. The idea is to pose the equations on a fixed domain. This method is thoroughly tested and validated in our study. By choosing specific values of spring parameters, this system can be used to damp (or in other words to extract the energy of) incident water waves.</p>
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