Vegetation meadows in coastal waters are a key constituent of a future green defense package due to the ecosystem services they provide and the potential to attenuate wave energy. To numerically describe the vegetation dynamics under wave action, this paper presents a novel application of a numerical coupling for solving fluid–elastic structure interactions (FSI) problems involving ultra-thin elements in a 3-D environment. The extended two-way coupling employed in this work combines the mesh-free Smoothed Particle Hydrodynamics (SPH) method in the DualSPHysics code to solve the fluid flow, and the Finite Element Analysis (FEA) structural solver in Project Chrono to solve the structural dynamics. To represent the vegetation, a flexible structure based on the Euler–Bernoulli beam model is used. The beam element is embedded into the SPH domain using an envelope subdomain that is discretized using dummy boundary particles. As such, this dummy envelope serves as a decoupling interface for the geometrical properties of the structure, allowing for ultra-thin structures smaller than the initial inter-particle distance (dp). The numerical approach is validated against an experimental setup including a flexible blade swaying under the action of an oscillatory flow. The results demonstrate that the numerical model is able to resolve the wave–vegetation interaction problem. Furthermore, additional insights into the blade dynamics reveal that the swaying velocity increases linearly along the length, with the upper part swaying at a speed comparable to the fluid velocity while the stem remains relatively stationary. Additionally, the findings indicate that rigid vegetation experiences higher forces per unit length, and in systems with substantial swaying motion, energy dissipation predominantly occurs around the lower base of the vegetation.

An improved Relaxation Zone (RZ) method has been implemented in the meshless SPH-based DualSPHysics model. Final purpose of this work is to have a general wave generation scheme that allows coupling SPH-based models to other models, e.g. Eulerian based wave models, besides employing the RZ as alternative wave generation in SPH as a stand-alone scheme. Using RZ in SPH, the movement of the fluid particles is controlled by correcting their orbital velocity by means of a weighting function in a specified generation area. In the present work, the new technique is used to couple DualSPHysics to the non-hydrostatic wave-flow model SWASH. The results of RZ employed both as stand-alone wave generation technique and as coupling framework with SWASH model are validated for wave generation and wave reflection for monochromatic waves. Then, the method is tested successfully for generation and absorption of irregular waves. Finally, the coupling between DualSPHysics and SWASH using RZ is validated against experimental data concerning the wave flow impacts on vertical walls. A procedure for a proper design of the RZ (i.e. shape of the weighting function, size of the RZ) is described in the present work. Overall, the results indicate that the proposed improved RZ technique is among the most effective alternatives for wave generation in SPH-based models for coastal engineering application.