Asymptotic‐preserving schemes for kinetic–fluid modeling of disperse two‐phase flows with variable fluid density

SUMMARY 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 schemes suited to such regimes. We extend the method introduced in [Goudon T, Jin S, Liu JG, Yan B. Journal of Computational Physics 2013; 246 :145‐164] to the case of variable density in compressible flow. We check the accuracy and the asymptotic‐preserving 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. Copyright © 2014 John Wiley & Sons, Ltd.