# Numerical modelling of surface water wave interaction with a moving wall

## TL;DR

This paper presents a numerical model for water wave interaction with a horizontally movable wall attached to springs, enabling wave energy damping through a semi-analytical finite difference method.

## Contribution

It introduces a novel semi-analytical numerical approach for simulating wave interaction with a spring-mounted moving wall, allowing energy extraction from incident waves.

## Key findings

- The method accurately models wave-wall interactions.
- Spring parameters can be tuned for wave energy damping.
- Validation confirms the model's reliability.

## Abstract

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.