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In this paper, a unified framework for particulate two-phase flow will bepresented with a wide range of solid-particle concentration from dilute todense 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-kineticwave-particle method (UGKWP) for the particle phase. The GKS is a second-orderNavier-Stokes flow solver for the continuum flow. The UGKWP is a multiscalemethod for all flow regimes. The wave and particle decomposition in UGKWPdepends on the cell's Knudsen number (Kn). At a small Kn number, the highconcentrated solid particle phase will be modeled by the Eulerian hydrodynamicwave due to the intensive particle-particle collisions. At a large Kn number,the dilute solid particle will be sampled and followed by the Lagrangianparticle formulation to capture the non-equilibrium transport. In thetransition regime, the distribution and evolution of particle and wave in UGKWPare controlled by the local Kn number with a smooth transition between theabove limits. In the current scheme, the two phase model improves the previousone in all following aspects: drag force model for different solid particleconcentrations; the frictional pressure in inter-particle contacts at highsolid-particle concentration; a flux limiting model to avoid solid particles'over-packing; additional non-conservative nozzle and work terms for the gasphase. Besides, the inter-particle collisions have been refined numerically forthe dense particle flow through the discretization of the collision term andnumerical flux function. The numerical scheme is tested in a series of typicalgas-particle problems. The results validate the accuracy and reliability of theproposed method for gas-particle flow.

Unified gas-kinetic wave-particle method for gas-particle two phase flow from dilute to dense solid-particle limit