## 1 Introduction  
Nowadays, numerical methods are becoming the main tool used by scientists and researchers to study fluid dynamics problems. Even if experimental investigations provide a lot of reliable data useful to calibrate numerical models, experimentation requires a lot of time to be planned and executed, usually at a high economical cost. Moreover, the results of experimental tests are limited to just a fixed number of points, while computational methods can provide the desired quantities in any point of the computational domain, allowing a better understanding of the physical phenomena under investigation. The numerical models for the study of a fluid motion could be based on two different approaches, the Eulerian or the Lagrangian method. The main difference between the two methodologies is that while a Eulerian method discretizes space into a fixed grid and finds the unknown variables at the nodal points, the latter discretizes the continuum into a certain number of moving nodes. Moreover, while in a Lagrangian approach the properties of the single fluid particle are studied in accordance with the initial spatial and temporal position, the Eulerian approach represents the distribution of these properties in a domain without referring to the history of the particle's trajectories. For example, from the experimental point of view, the PIV (Particle Image Velocimetry) technique allows reconstruction of the velocity vectors that occupy an instantaneous velocity field, based on the average particle motion in space [1; 2; 3]. Instead, from a Lagrangian viewpoint, PTV (Particle Tracking Velocimetry) traces the pathway of an individual particle from a sequence of images in a system. This method is better than PIV for handling non-stationary flow [4]. Eulerian approaches or grid-based methods such as the finite element method (FEM), finite difference method (FDM) and finite volume method (FVM) have been applied to a wide range of engineering applications such as breaking waves [5; 6; 7], eddies [8], hydraulic jumps [9; 10; 11; 12], sediment transport [13] and current and oil drift modeling [14; 15; 16; 17]. Despite their great success, grid-based methods suffer from some difficulties, in particular for those cases that present discontinuities or whose mesh needs to be modified during run time according to topological changes. For these reasons, during the last few years, research has been focused on the development of Lagrangian and meshless techniques, such as the discrete element method (DEM) [18], immersed particle method (IPM) [19], smoothed particle hydrodynamics (SPH) [20] and finite volume particle method (FVPM) [21]. Lagrangian methods have been successfully applied in different fields of fluid dynamics, such as free surface flows [22], the breaking and impact of waves [23; 24; 25; 26; 27], multiphase flows [28; 29], sediment transport [30; 31; 32], fluid-structure interaction problems [33; 34; 35], oscillating jets that induce breaking waves [36; 37; 38; 39] and hydraulic jumps [40; 41; 42; 43; 44; 45; 46]. New research challenges in Computational Fluid Dynamics (CFD) are currently evolving; in particular, recently, research has been focused on coupling the Eulerian- Lagrangian techniques to combine the advantages of the individual models in a single model, thus increasing the accuracy, efficiency and regime of validity. For example, the SPH code is also being coupled with the discrete element Method [47] or with the distributed contact discrete element method (DCDEM) [48] for fluid-solid modeling. The flow is described by the Navier-Stokes Equations and can be solved by using the two main classes of methods: finite element methods and meshfree methods. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation.