The Relaxation Zone method (RZ) has been implemented in the meshless SPH-based DualSPHysics code. RZ acts as an internal wave maker and allows coupling DualSPHysics with any other model or analytical solution to generate sea waves. In this work, the coupling with the SWASH model is performed to simulate multi-scale and long-duration phenomena in coastal engineering, which represent a challenge for researcher and practitioners. In fact, despite the fact that SPH-based models are getting more and more popular in coastal and civil engineering, they still present a huge computational cost. In the present work, RZ is validated for phenomena of overtopping flow impacts on vertical walls. The results proved that the RZ is efficient and reliable alternative for wave generation in SPH-based models for coastal engineering applications.
Smoothed Particle Hydrodynamics method (SPH) is a promising meshless technique for modelling fluid flows and fluid-structure interaction (FSI) as it is capable to deal with large deformations, complex geometries, violent free-surface flows inducing large abrupt hydrodynamic loads and highly nonlinear phenomena (Violeau, 2012).
In general, SPH methods can be categorized into two groups: weakly compressible and incompressible. The Weakly Compressible SPH (WCSPH) methods solve an appropriate equation of state (Tait's equation) in a fully explicit form. The DualSPHysics model used in the present work is based on WCSPH. The incompressible SPH (ISPH) methods (e.g. Shao & Lo, 2003) solve a Poisson pressure equation (PPE) by applying project-based methods. Latest advancements have been made during the last decade in the context of SPH methods in terms of model stability, accuracy, energy conservation, boundary conditions and improved simulations of multiphase flows and fluid-structure interactions. A comprehensive review of it is presented in Gotoh & Khayyer (2016, 2018).
SPH methods have been widely applied to coastal engineering problems, such as wave breaking (e.g. Khayyer et al., 2008), wave overtopping (e.g. Gómez-Gesteira et al., 2005), wave run-up (e.g. Zhang et al., 2018), wave impacts (e.g. Altomare et al., 2015), tsunamilike wave processes (e.g. St-germain et al., 2014), wave energy applications (e.g. Crespo et al., 2017). Notwithstanding, further research is still needed to enhance the reliability of SPH methods and to widen their applicability for coastal engineering problems. Lately Rota Roselli et al. (2018) presented an automatic optimization framework to find the set of SPH parameters in DualSPHysics for an accurate wave propagation modelling. Yet, there are still limitations to be solved, one of which consisting in the unphysical oscillations in the pressure field due to high-frequency acoustic noise. Meringolo et al. (2017) proposed a procedure to filter out this noise, however the work is dedicated to post-processing analysis rather than solve the problem a priori. For WCSPH, besides the most classical diffusion schemes such as artificial viscosity (Monaghan, 1992), the so-called δ-SPH scheme has been proposed (e.g. Molteni & Colagrossi, 2009) to increase accuracy of the pressure field. To improve both accuracy and stability in SPH, particle regularization schemes have been proposed in order to regularize the anisotropic distributions of particles prone to be formed due to Lagrangian characteristics of particle methods (Lind et al., 2012).
