  In this paper, a unified gas kinetic scheme for multiphase dilute
gas-particle system is proposed. The UGKS multiphase (UGKS-M) is a finite
volume method, which captures flow physics in the regimes from collisionless
multispecies transport to the two-fluid hydrodynamic Navier-Stokes (NS)
solution with the variation of Knudsen number, and from granular flow regime to
dusty gas dynamics with the variation of Stokes number. The main reason for
preserving the multiscale nature in UGKS-M is mainly coming from the direct
modeling 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 determines
flow behavior in different regimes. For the particle phase, the integral
solution of the kinetic equation is used in the construction of the numerical
flux, which takes into account the particle transport, collision, and
acceleration. The gas phase, which is assumed to be in the continuum flow
regime, evolves numerically by the gas kinetic scheme (GKS), which is a subset
of the UGKS for the Navier-Stokes (NS) solutions. The interaction between the
gas and particle phase is calculated based on a velocity space mapping method,
which solves accurately the kinetic acceleration process. The stability of
UGKS-M is determined by the CFL condition only. With the inclusion of the
material temperature evolution equation of solid particles, the UGKS-M
conserves the total mass, momentum, and energy for the whole multiphase system.
In the numerical tests, the UGKS-M shows good multiscale property in capturing
the particle trajectory crossing (PTC), particle wall reflecting phenomena, and
vortex-induced segregation of inertial particles under different Stokes
numbers. The scheme is also applied to simulate shock induced fluidization
problem and the simulation results agree well with experimental measurement.
