A novel interface method for two-dimensional multiphase SPH: Interface detection and surface tension formulation

Abstract A novel interface method is developed in this paper for two-dimensional smoothed particle hydrodynamics (SPH) modelings of multiphase flows. The present interface method aims to resolve two essential issues in the multiphase flow simulations: the interface detection and the implementation of surface tension force. Specifically, a novel and easy-to-implement algebraic indicator is proposed to detect the interface particles. And the surface tension force is locally implemented on the interface particles by reconstructing arc lines connecting three adjacent interface particles. Compared with the previous surface reconstruction method, the present method utilizes fewer particles in the local evaluation of surface tension. The novel algebraic indicator provides more accurate and efficient detection of the interface particles, especially for the sparse or aggregated particle distributions. In the meantime, the present surface tension formulation removes the tedious process of evaluating gradient of the color index and thus significantly improves the numerical efficiency. The accuracy, flexibility and efficiency of the present interface method are comprehensively evaluated through four numerical examples, namely the sloshing in a rectangular tank, oscillation of elliptic droplet, Laplace law for a stationary droplet, and air bubble rising in water. The good agreement of the present numerical results with the published results demonstrates that the novel interface method proposed in this paper can precisely detect the interface particles with appealing sharpness, and recover the surface tension force accurately and efficiently.