Exploiting Numerical Behaviors in SPH.

Smoothed Particle Hydrodynamics is a meshless particle method able to evaluate unknown field functions and relative differential operators. This evaluation is done by performing an integral representation based on a suitable smoothing kernel function which, in the discrete formulation, involves a set of particles scattered in the problem domain. Two fundamental aspects strongly characterizing the development of the method are the smoothing kernel function and the particle distribution. Their choice could lead to the so-called particle inconsistency problem causing a loose of accuracy in the approximation; several corrective strategies can be adopted to overcome this problem. This paper focuses on the numerical behaviors of SPH with respect to the consistency restoring problem and to the particle distribution choice, providing useful hints on how these two aspects affect the goodness of the approximation and moreover how they mutually influence themselves. A series of numerical studies are performed approximating 1D, 2D and 3D functions validating this idea.