An SPH model for multiphase flows with complex interfaces and large density differences

Abstract

In this paper, an improved SPH model for multiphase flows with complex interfaces and large density differences is developed. The multiphase SPH model is based on the assumption of pressure continuity over the interfaces and avoids directly using the information of neighboring particles' densities or masses in solving governing equations. In order to improve computational accuracy and to obtain smooth pressure fields, a corrected density re-initialization is applied. A coupled dynamic solid boundary treatment (SBT) is implemented both to reduce numerical oscillations and to prevent unphysical particle penetration in the boundary area. The density correction and coupled dynamics SBT algorithms are modified to adapt to the density discontinuity on fluid interfaces in multiphase simulation. A cut-off value of the particle density is set to avoid negative pressure, which can lead to severe numerical difficulties and may even terminate the simulations. Three representative numerical examples, including a Rayleigh–Taylor instability test, a non-Boussinesq problem and a dam breaking simulation, are presented and compared with analytical results or experimental data. It is demonstrated that the present SPH model is capable of modeling complex multiphase flows with large interfacial deformations and density ratios.