Journal of Scientific Computing

, Volume 74, Issue 1, pp 336–374 | Cite as

Numerical Simulation of Microflows Using Moment Methods with Linearized Collision Operator

  • Zhenning Cai
  • Manuel Torrilhon


Hyperbolic moment equations based on Burnett’s expansion of the distribution function are derived for the Boltzmann equation with linearized collision operator. Boundary conditions are equipped for these models, and it is proven that the number of boundary conditions is correct for a large class of moment models. A new second-order numerical scheme is proposed for solving these moment equations, and the new method is suitable for both ordered- and full-moment theories. Numerical experiments are carried out for both one- and two-dimensional problems to show the performance of the moment methods.


Hyperbolic moment equations Burnett’s expansion Linearized collision operator Maxwell’s boundary condition 



We thank Dr. Xiaojun Gu and Dr. Anirudh Rana for providing DSMC results for the two-dimensional problems. This research was supported by Humboldt Research Fellowship for Postdoctoral Researchers provided by Alexander von Humboldt Foundation.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Center for Computational Engineering ScienceRWTH Aachen UniversityAachenGermany

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