Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows

Thierry Goudon (1, 2) , Shi Jin (3) , Jian-Guo Liu (4) , Bokai Yan (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
3 DM - Department Mathematics
4 Duke Physics

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 Pois- sion and Helmholtz solvers are needed. Numerical experiments are presented to demonstrate the accuracy and asymptotic behavior of the schemes, with several interesting applications

Domaines: Equations aux dérivées partielles [math.AP]

Thierry Goudon, Shi Jin, Jian-Guo Liu, Bokai Yan. Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows. 2011. ⟨hal-00593658⟩