Assessment of the ellipsoidal-statistical Bhatnagar-Gross-Krook model for force-driven Poiseuille flows

Jian-Ping Meng, Lei Wu, Jason Reese, Yonghao Zhang

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We investigate the accuracy of the ellipsoidal-statistical Bhatnagar–Gross–Krook (ES-BGK) kinetic model for planar force-driven Poiseuille flows. Our numerical simulations are conducted using the deterministic discrete velocity method, for Knudsen numbers (Kn) ranging from 0.05 to 10. While we provide numerically accurate data, our aim is to assess the accuracy of the ES-BGK model for these flows. By comparing with data from the direct simulation Monte Carlo (DSMC) method and the Boltzmann equation, the ES-BGK model is found to be able to predict accurate velocity and temperature profiles in the slip flow regime (0:01 < Kn 6 0:1), for both low-speed and high-speed flows. In the transition flow
regime (0:1 < Kn 6 10), however, the model does not quantitatively capture the viscous heating effect.
LanguageEnglish
Pages385-395
JournalJournal of Computational Physics
Volume251
Early online date13 Jun 2013
DOIs
Publication statusPublished - 15 Oct 2013

Fingerprint

Knudsen number
Poiseuille Flow
laminar flow
Gross
Knudsen flow
Slip Flow
Direct Simulation Monte Carlo
Temperature Profile
Kinetic Model
Velocity Profile
slip flow
Boltzmann Equation
Simulation Methods
Monte Carlo method
Heating
Boltzmann equation
High Speed
Model
temperature profiles
low speed

Keywords

  • kinetic theory
  • gas dynamics
  • BGK model
  • ES-BGK model
  • S model

Cite this

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abstract = "We investigate the accuracy of the ellipsoidal-statistical Bhatnagar–Gross–Krook (ES-BGK) kinetic model for planar force-driven Poiseuille flows. Our numerical simulations are conducted using the deterministic discrete velocity method, for Knudsen numbers (Kn) ranging from 0.05 to 10. While we provide numerically accurate data, our aim is to assess the accuracy of the ES-BGK model for these flows. By comparing with data from the direct simulation Monte Carlo (DSMC) method and the Boltzmann equation, the ES-BGK model is found to be able to predict accurate velocity and temperature profiles in the slip flow regime (0:01 < Kn 6 0:1), for both low-speed and high-speed flows. In the transition flowregime (0:1 < Kn 6 10), however, the model does not quantitatively capture the viscous heating effect.",
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Assessment of the ellipsoidal-statistical Bhatnagar-Gross-Krook model for force-driven Poiseuille flows. / Meng, Jian-Ping; Wu, Lei; Reese, Jason; Zhang, Yonghao.

In: Journal of Computational Physics, Vol. 251, 15.10.2013, p. 385-395.

Research output: Contribution to journalArticle

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AU - Zhang, Yonghao

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AB - We investigate the accuracy of the ellipsoidal-statistical Bhatnagar–Gross–Krook (ES-BGK) kinetic model for planar force-driven Poiseuille flows. Our numerical simulations are conducted using the deterministic discrete velocity method, for Knudsen numbers (Kn) ranging from 0.05 to 10. While we provide numerically accurate data, our aim is to assess the accuracy of the ES-BGK model for these flows. By comparing with data from the direct simulation Monte Carlo (DSMC) method and the Boltzmann equation, the ES-BGK model is found to be able to predict accurate velocity and temperature profiles in the slip flow regime (0:01 < Kn 6 0:1), for both low-speed and high-speed flows. In the transition flowregime (0:1 < Kn 6 10), however, the model does not quantitatively capture the viscous heating effect.

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