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

Abstract

SUMMARYWe 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.

Global weak solution to the inhomogeneous Navier–Stokes–Vlasov equations

“…The paper [15] studied a similar problem numerically. In addition, there have been a lot of studies on hydrodynamic limits, and we refer the reader to [5,17,18,24] (and the references therein) where some scaling and convergence methods such as the compactness and relative entropy method were applied to investigate the hydrodynamic limits.…”

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

“…3. Other two-phase flow models, for example, the compressible flows [15] or the variable density incompressible flows [14], will also be studied in our future work.…”

Multifluid Flows: A Kinetic Approach

“…Similar models are used for the simulation of particle-laden flows in [1,2,33,34,35,41]. For the simpler case of thin sprays [33], asymptotic issues are discussed e. g. in [10,23,24], and schemes dedicated to these regimes are presented in [11,25,26,27].…”

“…We make the treatment of the drag force implicit because it is usually a stiff term in the model. Hence, our strategy follows the method introduced in [26,27], the new difficulties being related to the close-packing term and the fact that we account for the volume occupied by the particles at the scale of the fluid, which leads to the constraint α p + α f = 1 for defining the pressure. The latter is treated in the spirit of projection methods for incompressible viscous flows, as introduced by A. Chorin [12,13,14] and R. Temam [42].…”