On the use of numerical diffusive terms in weakly-compressible SPH schemes

An in-depth discussion on the use of numerical diffusive terms in SPH models has been performed. These terms are generally added inside the continuity equation in order to reduce the spurious numerical noise that affects the density and pressure fields in weakly-compressible SPH schemes. Specific focus has been given to the theoretical analysis of the diffusive term structure and to the choice of the integration scheme and Courant-Friedrick-Lewy number. The most widespread formulations, that is, those by Ferrari et al. [1], Molteni & Colagrossi [2] and Antuono et al. [3], have been studied in details, highlighting the main benefits and drawbacks.