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Gas Micro-Flow Modelling Based on Regularized 13-Moment-Equations

[+] Author Affiliations
Manuel Torrilhon

ETH Zurich, Zurich, Switzerland

Henning Struchtrup

University of Victoria, Victoria, BC, Canada

Paper No. MNHT2008-52274, pp. 43-51; 9 pages
doi:10.1115/MNHT2008-52274
From:
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer, Parts A and B
  • Tainan, Taiwan, June 6–9, 2008
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 0-7918-4292-4 | eISBN: 0-7918-3813-7
  • Copyright © 2008 by ASME

abstract

We summarize our recent contributions to the development of macroscopic transport equations for gas micro-flows. A combination of the Chapman-Enskog expansion and Grad’s moment method in kinetic theory of gases yields the Regularized 13-Moment-Equations (R13 equations). These equations overcome deficiencies of Grad’s equations or Burnett models. They are asymptotically of super-Burnett order, i.e., of third order in the Knudsen number and linearly stable for all wave frequencies. In addition, a complete set of boundary conditions can derived from the accommodation boundary conditions of the Boltzmann equations. Mathematically, more boundary conditions are required and they can be derived from the R13 system itself through coherence relations. We present micro-channel and shock wave simulations to prove that R13 is a reliable and efficient continuum model for micro-flows of gases with moderate Knudsen numbers.

Copyright © 2008 by ASME

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