A multi-phase SPH model based on Riemann solvers for simulation of jet breakup

The discontinuous physical properties of the multiphase flow interface lead to the numerical instability, especially for the multiphase flow problems with large density or viscosity ratios. Based on Riemann solution, a novel multiphase SPH model is presented. The momentum equation of the Riemann form is improved to calculate the physical viscosity of multiphase flow and decrease the Riemann dissipation. The solid-wall boundary is imposed by one-sided Riemann problem. In addition, a repulsive force and the surface tension are applied on both sides of the multiphase interface to keep the interface sharpness and consider the small-scale interface effect. Three cases, squared droplet oscillating, single bubble rising (with different density and viscosity ratios) and two-bubble rising examples, are simulated to demonstrate the accuracy and effectiveness of the proposed method in dealing with the multiphase flow problems with the wide range of density and viscosity ratios and with the complex interfaces. Finally, the jet breakup problems of steady jets and pulsating jets are studied using the present model. A detailed process of jet breakup is observed, the surface wave structure of liquid jet could be identified. The influence of jet parameters (surface tension, velocity amplitude and velocity period) on physical information of jet is analyzed.