Numerical diffusive terms in weakly-compressible SPH schemes

A discussion on the use of numerical diffusive terms in SPH models is proposed. Such terms are, generally, added in 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, highlighting the main benefits and drawbacks of the most widespread formulations. Finally, specific test cases have been used to compare such formulations and to confirm the theoretical findings.