  In this paper, a unified framework for particulate two-phase flow will be
presented with a wide range of solid-particle concentration from dilute to
dense limit. The two phase flow is simulated by two coupled flow solvers, i.e.,
the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic
wave-particle method (UGKWP) for the particle phase. The GKS is a second-order
Navier-Stokes flow solver for the continuum flow. The UGKWP is a multiscale
method for all flow regimes. The wave and particle decomposition in UGKWP
depends on the cell's Knudsen number (Kn). At a small Kn number, the high
concentrated solid particle phase will be modeled by the Eulerian hydrodynamic
wave due to the intensive particle-particle collisions. At a large Kn number,
the dilute solid particle will be sampled and followed by the Lagrangian
particle formulation to capture the non-equilibrium transport. In the
transition regime, the distribution and evolution of particle and wave in UGKWP
are controlled by the local Kn number with a smooth transition between the
above limits. In the current scheme, the two phase model improves the previous
one in all following aspects: drag force model for different solid particle
concentrations; the frictional pressure in inter-particle contacts at high
solid-particle concentration; a flux limiting model to avoid solid particles'
over-packing; additional non-conservative nozzle and work terms for the gas
phase. Besides, the inter-particle collisions have been refined numerically for
the dense particle flow through the discretization of the collision term and
numerical flux function. The numerical scheme is tested in a series of typical
gas-particle problems. The results validate the accuracy and reliability of the
proposed method for gas-particle flow.
