NR𝑥𝑥 Simulation of Microflows with Shakhov Model

Zhenning Cai*, Ruo Li, Zhonghua Qiao

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

30 Citations (Scopus)
30 Downloads (Pure)


In this paper, we propose a method to simulate the microflows with Shakhov model using the NR𝑥𝑥 method developed in [Z. Cai and R. Li, SIAM J. Sci. Comput., 32 (2010), pp. 2875- 2907; Z. Cai, R. Li, and Y. Wang, Commun. Comput. Phys., 11 (2012), pp. 1415-1438; Z. Cai, R. Li, and Y. Wang, J. Sci. Comput., to appear]. The equation under consideration is the Boltzmann equation with force terms, and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.

Original languageEnglish
Pages (from-to)A339-A369
Number of pages31
JournalSIAM Journal on Scientific Computing
Issue number1
Publication statusPublished - 7 Feb 2012

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Boundary conditions
  • Microflow
  • NRxx method
  • Shakhov model


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