Diffusive terms for the conservation of mass equation in SPH

Anomalous fluctuations in pressure associated with the Lagrangian smoothed particle hydrodynamics method (SPH) have recently been treated by introducing diffusive terms in the conservation of mass equation. Here, five consistency conditions are proposed for such diffusive terms; three that must be satisfied and two that add to the generality of the models. Each of the existing diffusive terms are reviewed and their consistency properties and relationships discussed and summarized to provide a guide for their usage. The equivalence of Riemann solver SPH formulations and conservation of mass equation diffusive terms is demonstrated in this paper. A practical application consisting of a simulation of a dam break flow is proposed to show the consistency properties and relationship of some of the diffusive terms discussed in the paper.