Modelling of surface tension force for free surface flows in ISPH method

Purpose - The purpose of this paper is to show how a surface tension model and an eddy viscosity based on the Smagorinsky sub-grid scale model, which belongs to the Large-Eddy Simulation (LES) theory for turbulent flow, have been introduced into ISPH (Incompressible smoothed particle hydrodynamics) method. In addition, a small modification in the source term of pressure Poisson equation has been introduced as a stabilizer for robust simulations. This stabilization generates a smoothed pressure distribution and keeps the total volume of fluid, and it is analogous to the recent modification in MPS. Design/methodology/approach - The surface tension force in free surface flow is evaluated without a direct modeling of surrounding air for decreasing computational costs. The proposed model was validated by calculating the surface tension force in the free surface interface for a cubic-droplet under null-gravity and the milk crown problem with different resolution models. Finally, effects of the eddy viscosity have been discussed with a fluid-fluid interaction simulation. Findings - From the numerical tests, the surface tension model can handle free surface tension problems including high curvature without special treatments. The eddy viscosity has clear effects in adjusting the splashes and reduces the deformation of free surface in the interaction. Finally, the proposed stabilization appeared in the source term of pressure Poisson equation has an important role in the simulation to keep the total volume of fluid. Originality/value - An incompressible smoothed particle hydrodynamics is developed to simulate milk crown problem using a surface tension model and the eddy viscosity.