A mixed Eulerian-Lagrangian simulation of nonlinear wave interaction with a fluid-filled membrane breakwater

Abstract

This paper introduces a time-domain potential flow method for simulating fully nonlinear wave interaction with a fluid-filled membrane mounted on the seabed. The numerical method is based on a mixed Eulerian-Lagrangian method, which tracks the free water surface and the membrane using a Lagrangian method and solves the flow fields inside and outside the membrane using an Eulerian method. To remove the numerical instability, a method that satisfies the no-flux condition on the membrane at any location and any time was developed to calculate the radial displacement of the membrane at every time step and a Fourier series expression for the radial displacement of the membrane was used to calculate the local curvature of the membrane accurately. Experimental results from an existing experimental study were used for model validation and verification. The response of the membrane and the nonlinear wave scattering were simulated. The simulation results show that the transmission coefficients of the fundamental waves, second harmonic free and locked waves approach zero when a resonant response of the membrane to waves occurs. Sample results of the simulated tension in the membrane and interior pressure are also included in the discussion.