condition is its obvious simplicity. However, several consistency issues shall be considered when this boundary technique is applied. That's in fact a heavy limitation on its potential applications. Fluid Extension Probably the most popular methodology, or at least the most traditional one, to impose boundary conditions in SPH, is Fluid Extension technique. Such technique is based on populating the compact support across the boundary with so-called ghost particles, conveniently imposing their field values. Along this line, the integral neglect methodology can be considered as a particular case of fluid extensions, where the field, , vanish outside the computational domain. The main benefit of this methodology is the simplicity, provided that the boundary contribution is computed as part of the bulk interactions. Also, this methodology has been deeply analyzed in the literature. On the other hand, deploying ghost particles in the truncated domain is not a trivial task, such that modelling complex boundary shapes becomes cumbersome. The 2 most popular approaches to populate the empty domain with ghost particles are Mirrored-Particles and Fixed-Particles. Boundary Integral The newest Boundary technique is the Boundary Integral methodology. In this methodology, the empty volume integral is replaced by a surface integral, and a renormalization: with the normal of the generic j-th boundary element. The surface term can be also solved considering a semi-analytic expression. Modelling physics Hydrodynamics Weakly compressible approach Another way to determine the density is based on the SPH smoothing operator itself. Therefore, the density is estimated from the particle distribution utilizing the SPH interpolation. To overcome undesired errors at the free surface through kernel truncation, the density formulation can again be integrated in time. The weakly compressible SPH in fluid dynamics is based on the discretization of the Navier–Stokes equations or Euler equations for compressible fluids. To close the system, an appropriate equation of state is utilized to link pressure and density . Generally, the so-called Cole equation (sometimes mistakenly referred to as the "Tait equation") is used in SPH. It reads where is the reference density and the speed of sound. For water, is commonly used. The background pressure is added to avoid negative pressure values. Real nearly incompressible fluids such as water are characterized by very high speed of sounds of the order . Hence, pressure information travels fast compared to the actual bulk flow, which leads to very small Mach numbers . The momentum equation leads to the following