A high order off-lattice kinetic method for high speed flows with a moderate Knudsen number

Research output: Contribution to journalConference Contribution

Abstract

In this work, in the framework of the discrete unified gas kinetic scheme, a high order off-lattice kinetic method is proposed for high speed rarefied gas flows. The velocity distribution function is expanded on the basis of the Hermite polynomial to a certain order to ensure the conservation of the corresponding moments. The sod shock tube problem and two dimensional lid-driven cavity flow in the hydrodynamic and early transition regimes are performed to assess the proposed method. In particular, the performance of third and fourth order of truncated Hermite polynomial associated with several on and off-lattice discrete velocity sets are evaluated. It is confirmed from the simulation results that, with the fourth order Hermite polynomial expansion the proposed method can accurately reproduce the thermal and fully compressible hydrodynamic flow. However, it is surprisingly found that the performance of D2Q16 is better than that of D2Q17, and is even better than those of D2Q37 and D2Q25 for flows in the early transition regime, suggesting that the even number of velocity points without the zero velocity seems to have a better capacity than the odd one in capturing rarefaction effect. This indicates that the molecular velocity space discretized without the zero velocity may be a promising way to reduce the number of velocity point.

LanguageEnglish
Article number130013
Number of pages7
JournalAIP Conference Proceedings
Volume2132
Issue number1
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

Knudsen flow
high speed
kinetics
polynomials
sod
hydrodynamics
methodology
cavity flow
rarefaction
gases
rarefied gases
shock tubes
lids
gas flow
speed
method
conservation
velocity distribution
distribution functions
cavity

Keywords

  • fluid mechanics
  • discrete unified gas kinetic scheme
  • compressible hydrodynamic flow

Cite this

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title = "A high order off-lattice kinetic method for high speed flows with a moderate Knudsen number",
abstract = "In this work, in the framework of the discrete unified gas kinetic scheme, a high order off-lattice kinetic method is proposed for high speed rarefied gas flows. The velocity distribution function is expanded on the basis of the Hermite polynomial to a certain order to ensure the conservation of the corresponding moments. The sod shock tube problem and two dimensional lid-driven cavity flow in the hydrodynamic and early transition regimes are performed to assess the proposed method. In particular, the performance of third and fourth order of truncated Hermite polynomial associated with several on and off-lattice discrete velocity sets are evaluated. It is confirmed from the simulation results that, with the fourth order Hermite polynomial expansion the proposed method can accurately reproduce the thermal and fully compressible hydrodynamic flow. However, it is surprisingly found that the performance of D2Q16 is better than that of D2Q17, and is even better than those of D2Q37 and D2Q25 for flows in the early transition regime, suggesting that the even number of velocity points without the zero velocity seems to have a better capacity than the odd one in capturing rarefaction effect. This indicates that the molecular velocity space discretized without the zero velocity may be a promising way to reduce the number of velocity point.",
keywords = "fluid mechanics, discrete unified gas kinetic scheme, compressible hydrodynamic flow",
author = "Peng Wang and Yonghao Zhang",
year = "2019",
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day = "5",
doi = "10.1063/1.5119633",
language = "English",
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}

A high order off-lattice kinetic method for high speed flows with a moderate Knudsen number. / Wang, Peng; Zhang, Yonghao.

In: AIP Conference Proceedings, Vol. 2132, No. 1, 130013, 05.08.2019.

Research output: Contribution to journalConference Contribution

TY - JOUR

T1 - A high order off-lattice kinetic method for high speed flows with a moderate Knudsen number

AU - Wang, Peng

AU - Zhang, Yonghao

PY - 2019/8/5

Y1 - 2019/8/5

N2 - In this work, in the framework of the discrete unified gas kinetic scheme, a high order off-lattice kinetic method is proposed for high speed rarefied gas flows. The velocity distribution function is expanded on the basis of the Hermite polynomial to a certain order to ensure the conservation of the corresponding moments. The sod shock tube problem and two dimensional lid-driven cavity flow in the hydrodynamic and early transition regimes are performed to assess the proposed method. In particular, the performance of third and fourth order of truncated Hermite polynomial associated with several on and off-lattice discrete velocity sets are evaluated. It is confirmed from the simulation results that, with the fourth order Hermite polynomial expansion the proposed method can accurately reproduce the thermal and fully compressible hydrodynamic flow. However, it is surprisingly found that the performance of D2Q16 is better than that of D2Q17, and is even better than those of D2Q37 and D2Q25 for flows in the early transition regime, suggesting that the even number of velocity points without the zero velocity seems to have a better capacity than the odd one in capturing rarefaction effect. This indicates that the molecular velocity space discretized without the zero velocity may be a promising way to reduce the number of velocity point.

AB - In this work, in the framework of the discrete unified gas kinetic scheme, a high order off-lattice kinetic method is proposed for high speed rarefied gas flows. The velocity distribution function is expanded on the basis of the Hermite polynomial to a certain order to ensure the conservation of the corresponding moments. The sod shock tube problem and two dimensional lid-driven cavity flow in the hydrodynamic and early transition regimes are performed to assess the proposed method. In particular, the performance of third and fourth order of truncated Hermite polynomial associated with several on and off-lattice discrete velocity sets are evaluated. It is confirmed from the simulation results that, with the fourth order Hermite polynomial expansion the proposed method can accurately reproduce the thermal and fully compressible hydrodynamic flow. However, it is surprisingly found that the performance of D2Q16 is better than that of D2Q17, and is even better than those of D2Q37 and D2Q25 for flows in the early transition regime, suggesting that the even number of velocity points without the zero velocity seems to have a better capacity than the odd one in capturing rarefaction effect. This indicates that the molecular velocity space discretized without the zero velocity may be a promising way to reduce the number of velocity point.

KW - fluid mechanics

KW - discrete unified gas kinetic scheme

KW - compressible hydrodynamic flow

U2 - 10.1063/1.5119633

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JO - AIP Conference Proceedings

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