Asymptotic‐preserving schemes for kinetic–fluid modeling of disperse two‐phase flows with variable fluid density. (14th February 2014)

• Record Type: Journal Article
• Authors: Goudon, Thierry; Jin, Shi; Liu, Jian‐Guo; Yan, Bokai
• Is Part Of: International journal for numerical methods in fluids. Volume 75:Number 2(2014:May)
• Page Start: 81
• Page End: 102
• Publication Date: 2014-02-14
• Subjects: Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.3885
• Languages: English
• ISSNs: 0271-2091

Abstract

<abstract abstract-type="main" id="fld3885-abs-0001"> <title>SUMMARY</title> <p id="fld3885-para-0001">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. <italic>Journal of Computational Physics</italic> 2013; <bold>246</bold>: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 &amp; Sons, Ltd.</p> </abstract>