  In this paper, a unified algorithm will be proposed for the study of
gas-solid particle multiphase flow. The gas-kinetic scheme (GKS) is used to
simulate the continuum gas phase and the multiscale unified gas-kinetic
wave-particle (UGKWP) method is developed for the multiple dispersed solid
particle phase. At the same time, the momentum and energy exchanges between
gas-particle phases will be included under the GKS-UGKWP framework. For each
disperse solid particle phase, the decomposition of deterministic wave and
statistic particle in UGKWP is based on the local cell's Knudsen number. This
is very significant for simulating dispersed particle phases at different
Knudsen numbers due to the variation of physical properties in individual
particle phase, such as the particle diameter, material density, and the
corresponding mass fraction inside each control volume. For the gas phase, the
GKS is basically an Eulerian approach for the NS solution. Therefore, the
GKS-UGKWP method for the gas-particle flow unifies the Eulerian-Eulerian (EE)
and Eulerian-Lagrangian (EL) methods. An optimal strategy can be obtained for
the solid particle phase with the consideration of physical accuracy and
numerical efficiency. Two cases of gas-solid fluidization system, i.e., one
circulating fluidized bed and one turbulent fluidized bed, are simulated. The
typical flow structures of the fluidized particles are captured, and the
time-averaged variables of the flow field agree well with the experimental
measurements. In addition, the shock particle-bed interaction is studied by the
proposed GKS-UGKWP, which validates the method for polydisperse gas-particle
system in the supersonic case, where the dynamic evolution process of the
particle cloud is investigated.
