Abstract: Abstract: In the simulation of multiphase flow using the smoothed particle hydrodynamics (SPH) method, the density of the multiphase flow at the interface was discontinuous, the pressure calculation of the particle interface was erroneous, and problems occurred, such as pressure oscillation at the interface and interface fracture. In response to the above problems, a new pressure gradient approximation formula and an improved artificial repulsion formula at the interface were proposed to make the interface clearer and smoother without penetration, thus producing better simulation results. In addition, by giving a color function calculation formula based on density weights, the formula was improved for the calculation of surface tension at the interface of multiphase flow with high density ratio, leading to the smoother density transition of multiphase flow interface and better simulation effect. Finally, through three simulation experiments, such as dam break, Rayleigh-Taylor interface instability, and non-Boussinesq locked exchange problem, the particle distribution map of the interface and the distance of the interface front at different times were obtained. The results can verify the rationality of the new pressure gradient approximation formula and the artificial repulsion formula at the interface. Through the simulation experiment of droplet formation in the air, the particle change diagram formed by the circular droplet was obtained, and the result can corroborate the effectiveness of the improved surface tension calculation method in this paper

Key words: Keywords: smoothed particle hydrodynamics method, multi-phase flow, pressure gradient particle approximation, artificial repulsion, the color function, surface Tension