Goudon, T; Jin, S; Liu, J-G; Yan, B, *Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows*,
Journal of Computational Physics, vol. 246
(2013),
pp. 145-164 [doi] .
**Abstract:**

*We consider a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation. Such a problem arises in the description of particulate flows. We design a numerical scheme to simulate the behavior of the system. This scheme is asymptotic-preserving, thus efficient in both the kinetic and hydrodynamic regimes. It has a numerical stability condition controlled by the non-stiff convection operator, with an implicit treatment of the stiff drag term and the Fokker-Planck operator. Yet, consistent to a standard asymptotic-preserving Fokker-Planck solver or an incompressible Navier-Stokes solver, only the conjugate-gradient method and fast Poisson and Helmholtz solvers are needed. Numerical experiments are presented to demonstrate the accuracy and asymptotic behavior of the scheme, with several interesting applications. © 2013 Elsevier Inc.*