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Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

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.