Energy-conserving formulation of the CSF model for the simulation of surface tension at fluid-fluid interfaces with smoothed particle hydrodynamics

Abstract

Numerical modeling of surface tension requires an accurate description of fluid-fluid interfaces as well as an efficient discretization of the governing equations. As a Lagrangian method, smoothed particle hydrodynamics (SPH) is therefore well-suited for modeling of surface tension, since any movement of the interface is naturally incorporated. However, current surface-tension formulations based on the Continuum Surface Force (CSF) model suffer from spurious currents near the interface which lead to mixing of fluids and can cause instabilities, especially for low viscosities. In this work, we propose a new discretization of the CSF model which conserves the total energy of the fluid, suppressing the aforementioned spurious currents successfully. In numerical tests, the new discretization is compared to analytical solutions and current formulations of the CSF model, showing the improved accuracy and convergence and, hence, stability of the new method as a consequence of the reduced spurious currents.