Asymptotic - Preserving schemes for kinetic – fluid modeling of disperse two - phase flows with variable fluid density ∗

We are concerned with a coupled system describing the interaction between suspended particles and a dense fluid. The particles are modeled by a kinetic equation of Vlasov-Fokker-Planck type, and the fluid is described by the incompressible Navier-Stokes system, with variable density. The systems are coupled through drag forces. High friction regimes lead to a purely hydrodynamic description of the mixture. We design first and second order asymptotic-preserving (AP) schemes suited to such regimes. We extend the method introduced in [10] to the case of variable density in compressible flow. We check the accuracy and the AP property numerically. We set up a few numerical experiments to demonstrate the ability of the scheme in capturing intricate interactions between the two phases on a wide range of physical parameters and geometric situations.