Comparative study of the discrete velocity and the moment method for rarefied gas flows

Weiqi Yang, Xiao Jun Gu, David Emerson, Yonghao Zhang, Shuo Tang

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Abstract

In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. However, it is usually computationally expensive in dealing with complex geometry and high Mach number flows. In the present work, both classical third-order time implicit DVM and the moment method are employed in finding steady-state solutions of the force-driven Poiseuille flow and flow past a circle cylinder. Their performance, in terms of accuracy, has been compared and analyzed. Choosing the velocity distribution functions (VDFs) obtained from DVM solutions as the benchmark, we reconstruct the expanded VDFs using regularized 13 moment equations (R13) and regularized 26 moment equations (R26) and then compare the accuracy of the expanded VDFs with different order of Hermite polynomial expansions. From the computed velocity profiles and reconstructed VDFs, we have found that the moment method can extend the macroscopic equations into the early transition regime, and the R26 can relatively accurately represent the characteristics of the VDFs in comparison with the gas kinetic model. Conversely, the Navier-Stokes-Fourier (NSF) equations are not able to produce an accurate description of the expanded distribution functions.

Original languageEnglish
Article number120006
Number of pages9
JournalAIP Conference Proceedings
Volume2132
DOIs
Publication statusPublished - 5 Aug 2019
Event31st International Symposium on Rarefied Gas Dynamics, RGD 2018 - Glasgow, United Kingdom
Duration: 23 Jul 201827 Jul 2018

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Keywords

  • rarefied gas dynamics
  • discrete velocity method
  • DVM
  • velocity distribution functions
  • VDF
  • gas kinetic model

Cite this

Yang, W., Gu, X. J., Emerson, D., Zhang, Y., & Tang, S. (2019). Comparative study of the discrete velocity and the moment method for rarefied gas flows. AIP Conference Proceedings, 2132, [120006]. https://doi.org/10.1063/1.5119619