We have developed a numerical simulation scheme combining a vortex method and a particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. It is a completely grid-free Lagrangian–Lagrangian simulation, which is able to simulate the primary effect of vortical flow on the unsteady particle motion and dispersion. It can handle unsteady high Reynolds number flows. So far, no one has applied this kind of method internal multiphase flows, though many industrial multiphase flows are internal. In this study, internal liquid-solid two-phase flows in a vertical channel and a mixing tee have been calculated by the new method, in which use of the vortex introduction model enables the simulation of the dynamic behavior of separation or reattachment. In the mixing tee, solid particle phenomena such as depositions or particle-wall collisions have been simulated and measured. Numerical results based on simple two-dimensional flow and one-way model show good agreement with the experimental data. The results show that turbulent vortices dominate particle motion. It has been shown that the present method can be useful in the design of industrial multiphase flows with particle mixing, dispersion, deposition, and particle-wall collision because it is possible to simulate the effect of turbulent vortices on the particle motion.