A study on the energy consistency in SPH surface tension modelling

In the present work the evolution of viscous drops oscillating under the action of surface tension is tackled. Thanks to its structure, the SPH scheme allows for an analysis of the energy balance that is rarely addressed to in the general Computational Fluid Dynamics literature for this kind of flows. A procedure for checking the consistency between the energy of the surface-tension force and the free-surface evolution is proposed. Such a procedure relies on well-known analytical relations for the surface tension and on the evaluation of the free-surface area through a level-set function. Several test cases, in both two and three dimensional frameworks, are considered for validation. The study is performed by selecting a specific SPH scheme with a specific single-phase surface tension model. In any case, the procedure proposed is general and extendable to other SPH surface tension models and SPH schemes.