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

A unified framework for particulate two-phase flow is presented with a wide range of solid particle concentration from dilute to dense limit. The simulated by two coupled solvers, that is, the gas-kinetic scheme (GKS) gas phase and wave–particle method (UGKWP) phase. GKS second-order Navier–Stokes solver. UGKWP multiscale all regimes. wave decomposition in depends on cell's Knudsen number (Kn). At small Kn number, highly concentrated will be modeled Eulerian hydrodynamic due intensive particle–particle collisions. large followed Lagrangian capture non-equilibrium transport. In transition regime, smooth between above limits obtained according local number. distribution particles composed analytical function discrete particle, both condensed phases can automatically captured most efficient way. current scheme, model improves previous one many aspects, such as drag force model, frictional pressure formulation, flux limiting model. tested typical gas–particle problems, including interaction shock layer, horizontal pneumatic conveying, bubble formation, cluster phenomena fluidized bed. results validate GKS-UGKWP simulation flow.