A comparative study of discrete velocity methods for low-speed rarefied gas flows

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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. Although various versions of DVM have been developed, their performance, in terms of modeling accuracy and computational efficiency, is yet to be comprehensively studied in all the flow regimes. Here, the traditional third-order time-implicit Godunov DVM (GDVM) and the recently developed discrete unified gas-kinetic scheme (DUGKS) are analysed in finding steady-state solutions of the low-speed force-driven Poiseuille and lid-driven cavity flows. With the molecular collision and free streaming being treated simultaneously, the DUGKS preserves the second-order accuracy in the spatial and temporal discretizations in all flow regimes. Towards the hydrodynamic flow regime, not only is the DUGKS faster than the GDVM when using the same spatial mesh, but also requires less spatial resolution than that of the GDVM to achieve the same numerical accuracy. From the slip to free molecular flow regimes, however, the DUGKS is slower than the GDVM, due to the complicated flux evaluation and the restrictive time step which is smaller than the maximum effective time step of the GDVM. Therefore, the DUGKS is preferable for problems involving different flow regimes, particularly when the hydrodynamic flow regime is dominant. For highly rarefied gas flows, if the steady-state solution is mainly concerned, the implicit GDVM, which can boost the convergence significantly, is a better choice.
LanguageEnglish
Pages33-46
Number of pages14
JournalComputers and Fluids
Volume161
Early online date13 Nov 2017
DOIs
StatePublished - 15 Jan 2018

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Kinetic theory of gases
Digital voltmeters
Flow of gases
Hydrodynamics
Gas dynamics
Computational efficiency
Fluxes

Keywords

  • gas kinetic equation
  • rarefied flow
  • discrete velocity method
  • discrete unified gas kinetic scheme

Cite this

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title = "A comparative study of discrete velocity methods for low-speed rarefied gas flows",
abstract = "In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. Although various versions of DVM have been developed, their performance, in terms of modeling accuracy and computational efficiency, is yet to be comprehensively studied in all the flow regimes. Here, the traditional third-order time-implicit Godunov DVM (GDVM) and the recently developed discrete unified gas-kinetic scheme (DUGKS) are analysed in finding steady-state solutions of the low-speed force-driven Poiseuille and lid-driven cavity flows. With the molecular collision and free streaming being treated simultaneously, the DUGKS preserves the second-order accuracy in the spatial and temporal discretizations in all flow regimes. Towards the hydrodynamic flow regime, not only is the DUGKS faster than the GDVM when using the same spatial mesh, but also requires less spatial resolution than that of the GDVM to achieve the same numerical accuracy. From the slip to free molecular flow regimes, however, the DUGKS is slower than the GDVM, due to the complicated flux evaluation and the restrictive time step which is smaller than the maximum effective time step of the GDVM. Therefore, the DUGKS is preferable for problems involving different flow regimes, particularly when the hydrodynamic flow regime is dominant. For highly rarefied gas flows, if the steady-state solution is mainly concerned, the implicit GDVM, which can boost the convergence significantly, is a better choice.",
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author = "Peng Wang and Ho, {Minh Tuan} and Lei Wu and Zhaoli Guo and Yonghao Zhang",
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A comparative study of discrete velocity methods for low-speed rarefied gas flows. / Wang, Peng; Ho, Minh Tuan; Wu, Lei; Guo, Zhaoli; Zhang, Yonghao.

In: Computers and Fluids, Vol. 161, 15.01.2018, p. 33-46.

Research output: Contribution to journalArticle

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