Modified Algorithm for Surface Tension with Smoothed Particle Hydrodynamics and Its Applications

Based on smoothed particle hydrodynamics (SPH) method with surface tension proposed by Morris, this paper is intended to modify equations for surface tension by modifying normal and curvature with corrective smoothing particle method (CSPM). Compared with the continuum surface force (CSF) model for surface tension employed in the traditional SPH method, the accuracy in the present paper is much higher in terms of handling the problems with large deformation and surface tension. The reason is that in the traditional SPH method the deficiency of particles is near the boundary and sharp-angled areas, and it causes gross errors of curvature calculation. Via a semicircular problem the new method is tested, the factors affecting the accuracy of which are then investigated, including surface definition, normal calculation and curvature calculation and smoothing length in curvature calculation is also confirmed reasonable. Furthermore, evolution of a liquid drop under surface tension from initial square shape is simulated by the new method. Compared with Morris method and grid-based volume of fluid method, there is higher accuracy at sharp-angled areas and the final particle distribution is more homogeneous. Then, based on the modified algorithm, coalescence process of two oil drops in water under surface tension is simulated. The results show a good agreement with physical process. The method presented here is more applicable to solve the surface tension problems in both vacuum and multi-phase fluid involving density differences. Moreover, second breakup of an oil drop in water accelerated by an impulsive force is analyzed through simulation.