Two-particle method for liquid–solid two-phase mixed flow

Liquid–solid two-phase flows are a very important class of multiphase flow problems widely existing in industry and nature. This paper establishes a two-phase model for liquid–solid two-phase flows considering multiphase states of granular media. The volume fraction is defined by the solid phase, determining the material properties of the two phases, and momentum is exchanged between the phases by drag and pressure gradient forces. On this basis, a two-particle method for simulating the liquid–solid two-phase flow is proposed by coupling smoothed particle hydrodynamics with smoothed discrete particle hydrodynamics. The coupling framework for the two-particle method is constructed, and the coupling between the algorithms is realized through interphase momentum exchange, volume fraction constraint, and field variable sharing. The liquid phase density changes are divided into two types. One is caused by weak compressibility, and the other is caused by changes in the solid phase volume fraction. The former is used to calculate the liquid-phase flow field, and the latter is used to calculate the two-phase coupling to solve the problem of sudden bulk density changes in the liquid phase caused by changes in particle volume fractions. The two-particle method maintains the dual advantages of the particle method for free interface tracking and material point tracking for particles. The new method is validated using a series of fundamental test cases, and comparison with experimental results shows that the new method is suitable for resolving liquid–solid two-phase flow problems and has significant practical value for future simulations of mudflow motions, coastal breakwaters, and landslide surges.