  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.
