Gas-kinetic scheme for compressible gas-particle system with coarse grained discrete element method

The existence of gas-particle multiphase flows is frequently observed in both natural and engineering fields. The multi-scale characteristic of gas-particle multiphase flows leads to difficulties in experiments and theoretical research, and the numerical simulations are playing an important role. In this paper, the gas-kinetic scheme (GKS) is extended for the gas-particle system by coupling with the coarse grained discrete element method. The novel method can be capable of handling gas-particle multiphase flows in various flow regimes from dilute, pattern-transition to dense particle flows. Different from the classical numerical methods based on Riemann fluxes, GKS presents a gas evolution process from kinetic scale to hydrodynamic scale and becomes robust for flows with strong discontinues, which is specially important for high-speed gas-particle flow. Meanwhile, GKS includes both the normal and tangential variations in the numerical fluxes, which simulates the complex flow field structures better. These advantages are beneficial for simulating compressible multiphase gas-particle flows with shock waves. Numerical examples from one-dimensional to three-dimensional cases are presented to validate the current scheme, and the numerical results agree well with the experimental and theoretical results.