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

Thierry Goudon INRIA Sophia Antipolis Méditerranée and Labo. J. A. Dieudonné Shi Jin Institute of Natural Sciences, and Ministry of Education Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University Jian-Guo Liu Duke University Bokai Yan University of California, Los Angeles

Analysis of PDEs mathscidoc:1702.03036

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 75, (1), 81–102, 2014.2
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.
Fluid–particles flows; Hydrodynamic regimes; Asymptotic preserving schemes; Kinetic-fluid model; Two-phase flow
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@inproceedings{thierry2014asymptotic-preserving,
  title={Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density},
  author={Thierry Goudon, Shi Jin, Jian-Guo Liu, and Bokai Yan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208104007396177310},
  booktitle={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},
  volume={75},
  number={1},
  pages={81–102},
  year={2014},
}
Thierry Goudon, Shi Jin, Jian-Guo Liu, and Bokai Yan. Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density. 2014. Vol. 75. In INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS. pp.81–102. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208104007396177310.
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