Macroscopic fluid modes with localized kinetic upscaling effects

PIERRE DEGOND Universit´e Paul Sabatier Jian-Guo Liu University of Maryland LUC MIEUSSENS Universit´e Paul Sabatier

Analysis of PDEs mathscidoc:1702.03060

MULTISCALE MODEL. SIMUL, 5, (3), 940–979, 2006.6
This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the nonequilibrium part of the distri-bution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretize our models, and several numerical examples are used to validate the method.
kinetic-fluid coupling, kinetic equation, hydrodynamic approximation, diffusion
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@inproceedings{pierre2006macroscopic,
  title={Macroscopic fluid modes with localized kinetic upscaling effects},
  author={PIERRE DEGOND, Jian-Guo Liu, and LUC MIEUSSENS},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209090820432304360},
  booktitle={MULTISCALE MODEL. SIMUL},
  volume={5},
  number={3},
  pages={940–979},
  year={2006},
}
PIERRE DEGOND, Jian-Guo Liu, and LUC MIEUSSENS. Macroscopic fluid modes with localized kinetic upscaling effects. 2006. Vol. 5. In MULTISCALE MODEL. SIMUL. pp.940–979. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209090820432304360.
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