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

Research output: Contribution to journalConference Contribution

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.

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

Fingerprint

rarefied gases
gas flow
comparative study
velocity distribution
distribution functions
gases
moments
rarefied gas dynamics
methodology
macroscopic equations
gas
laminar flow
kinetic equations
Mach number
kinetics
method
polynomials
velocity profile
distribution
expansion

Keywords

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

Cite this

@article{03895befb2db4415a113b6603d3a92d8,
title = "Comparative study of the discrete velocity and the moment method for 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. 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.",
keywords = "rarefied gas dynamics, discrete velocity method, DVM, velocity distribution functions, VDF, gas kinetic model",
author = "Weiqi Yang and Gu, {Xiao Jun} and David Emerson and Yonghao Zhang and Shuo Tang",
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Comparative study of the discrete velocity and the moment method for rarefied gas flows. / Yang, Weiqi; Gu, Xiao Jun; Emerson, David; Zhang, Yonghao; Tang, Shuo.

In: AIP Conference Proceedings, Vol. 2132, 120006, 05.08.2019.

Research output: Contribution to journalConference Contribution

TY - JOUR

T1 - Comparative study of the discrete velocity and the moment method for rarefied gas flows

AU - Yang, Weiqi

AU - Gu, Xiao Jun

AU - Emerson, David

AU - Zhang, Yonghao

AU - Tang, Shuo

PY - 2019/8/5

Y1 - 2019/8/5

N2 - 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.

AB - 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.

KW - rarefied gas dynamics

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KW - gas kinetic model

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