  In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the
disperse dilute gas-particle multiphase flow is proposed. The gas phase is
always in the hydrodynamic regime. However, the particle phase covers different
flow regimes from particle trajectory crossing to the hydrodynamic wave
interaction with the variation of local particle phase Knudsen number. The
UGKWP is an appropriate method for the capturing of the multiscale transport
mechanism in the particle phase through its coupled wave-particle formulation.
In the regime with intensive particle collision, the evolution of solid
particle will be followed by the analytic wave with quasi-equilibrium
distribution; while in the rarefied regime the non-equilibrium particle phase
will be captured through particle tracking and collision, which plays a
decisive role in recovering particle trajectory crossing behavior. The
gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the
highly collision regime for the particles, no particles will be sampled in
UGKWP and the wave formulation for solid particle with the hydrodynamic gas
phase will reduce the system to the two-fluid Eulerian model. On the other
hand, in the collisionless regime for the solid particle, the free transport of
solid particle will be followed in UGKWP, and coupled system will return to the
Eulerian-Lagrangian formulation for the gas and particle. The scheme will be
tested for in all flow regimes, which include the non-equilibrium particle
trajectory crossing, the particle concentration under different Knudsen number,
and the dispersion of particle flow with the variation of Stokes number. A
experiment of shock-induced particle bed fluidization is simulated and the
results are compared with experimental measurements. These numerical solutions
validate suitability of the proposed scheme for the simulation of gas-particle
multiphase flow.
