On the use of an alternative water state equation in SPH

In this work new equations of state for water are formulated, they improve both the consistency and the accuracy of the Smoothed Particles Hydrodynamics (SPH) method to treat incompressible fluid dynamics. When, both physical and artificial viscous terms are introduced, entropy increases. In liquids, the influence of this entropy variation is negligible, but common SPH formulations treats the water as a weakly compressible gas. Therefore, for violent fluid motions, this increase cannot be neglected anymore and the energy equation has to be introduced. This equation has been time integrated, and connected to alternative water state equations which have been studied heuristically. These equations contain explicitly an internal energy term which increases largely especially during impact phenomena. The new numerical scheme adopted presents free parameters that are to be set. A plausible value of them has been evaluated in the case of the dambreak problem with violent fluid/structure and fluid/fluid interactions.