Generalized entropically damped artificial compressibility for weakly compressible SPH

This paper presents a formulation of a general form of an equation for pressure using thermodynamic principles. The motivation for this is in large part due to the need for a pressure equation for smoothed particle hydrodynamics, SPH, that takes into account the role of entropy. This is necessary because the use of physical and artificial viscosity leads to an increase in entropy. While such an increase in entropy in liquids may be negligibly small, standard SPH formulations treat a liquid as a weakly compressible gas. Consequently, for fluid-fluid and fluid-structure impact flows, the resulting increase in entropy is not negligible anymore. The proposed pressure equation contains diffusion terms whose main role is to smooth out unphysically large numerical oscillations in the pressure field related to the shock during an impact event. One consequence of adopting this numerical scheme, however, is that there are new (free) parameters that must be set. Nevertheless, effort has been made to obtain their plausible estimators from physical principles. The proposed model is also applicable outside the domain of SPH.