A Novel BEM–FEM Scheme for the Interaction of Water Waves with Multiple Vertical Cylinders in the Presence of Currents

The interaction of waves and currents with marine structures finds interesting applications, including the study of offshore and shoreline protection systems, as in the case of permeable breakwaters. The latter systems exhibit various benefits, including a decrease in wave run-up, reflected wave energy and load excitation, allowing for the propagation of part of the incident flow to the lee side, facilitating the improvement of water quality in the protected areas. The present work focuses on the modelling and numerical simulation of wave fields, interacting with arrays of vertical cylinders in the presence of currents. The problem is treated in the framework of potential theory in the frequency domain, assuming waves of small steepness, in conjunction with boundary integral formulation. Numerical results are presented and discussed, concerning the structure of the reflected and transmitted 3D flow fields, making the model suitable for optimization purposes; however, it presents increased computational cost. On the other hand, for small current velocities the problem can be approximately considered on the horizontal plane, modelled by the 2D Helmholtz equation with variable coefficients, which is numerically treated by a coupled BEM–FEM scheme. Numerical examples are presented, demonstrating that the latter model is cost-efficient, providing reasonable predictions, and can be used for the preliminary study of the hydrodynamic characteristics of the considered configurations and the support of the design.