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In this paper, a unified gas kinetic scheme for multiphase dilutegas-particle system is proposed. The UGKS multiphase (UGKS-M) is a finitevolume method, which captures flow physics in the regimes from collisionlessmultispecies transport to the two-fluid hydrodynamic Navier-Stokes (NS)solution with the variation of Knudsen number, and from granular flow regime todusty gas dynamics with the variation of Stokes number. The main reason forpreserving the multiscale nature in UGKS-M is mainly coming from the directmodeling of the flow physics in the scales of discrete cell size and time step,where the ratio of the time step over the particle collision time determinesflow behavior in different regimes. For the particle phase, the integralsolution of the kinetic equation is used in the construction of the numericalflux, which takes into account the particle transport, collision, andacceleration. The gas phase, which is assumed to be in the continuum flowregime, evolves numerically by the gas kinetic scheme (GKS), which is a subsetof the UGKS for the Navier-Stokes (NS) solutions. The interaction between thegas and particle phase is calculated based on a velocity space mapping method,which solves accurately the kinetic acceleration process. The stability ofUGKS-M is determined by the CFL condition only. With the inclusion of thematerial temperature evolution equation of solid particles, the UGKS-Mconserves the total mass, momentum, and energy for the whole multiphase system.In the numerical tests, the UGKS-M shows good multiscale property in capturingthe particle trajectory crossing (PTC), particle wall reflecting phenomena, andvortex-induced segregation of inertial particles under different Stokesnumbers. The scheme is also applied to simulate shock induced fluidizationproblem and the simulation results agree well with experimental measurement.

A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows VI: Dilute Disperse Gas-Particle Multiphase System