Abstract

In this work we present the mathematical model and simulations of a particular wave energy converter, the so-called oscillating water column. In this device, waves governed by the one-dimensional nonlinear shallow water equations arrive from offshore, encounter a step in the bottom and then arrive into a chamber to change the volume of the air to activate the turbine. The system is reformulated as two transmission problems: one is related to the wave motion over the stepped topography and the other one is related to the wave-structure interaction at the entrance of the chamber. We finally use the characteristic equations of Riemann invariants to obtain the discretized transmission conditions and we implement the Lax-Friedrichs scheme to get numerical solutions.

Highlights

  • General setting This work is devoted to model and simulate an on-shore oscillating water column (OWC), which is a particular type of wave energy converter (WEC) that transforms the energy of waves reaching the shore into electric energy

  • In this work the wave energy converter is deployed with stepped bottom, which means that incoming waves encounter a step in the bottom topography just before reaching the structure

  • Our goal is to numerically study this type of WEC considering as the governing equations for this wave-structure interaction the nonlinear shallow water equations derived by Lannes in [8], whose local well-posedness was obtained by Iguchi and Lannes in [7] in

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Summary

Introduction

Our goal is to numerically study this type of WEC considering as the governing equations for this wave-structure interaction the nonlinear shallow water equations derived by Lannes in [8], whose local well-posedness was obtained by Iguchi and Lannes in [7] in.

Organization of the paper
Notations
Governing equations
Derivation of the transmission conditions
At the topography step
At the structure side-walls
Reformulation as two transmission problems
Riemann invariants
Discretization of the model
Discretization of the equation
Discretization of the boundary conditions
Numerical validations
Numerical solutions
Accuracy analysis
Findings
Absorbed power and efficiency

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