Approximate kinetic equations in rarefied gas theory

Шахов, Е. М.

doi:10.1007/bf01016254

Cited by 58 publications

(33 citation statements)

References 7 publications

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“…To demonstrate the accuracy of our numerical method, we consider the sound propagation between two parallel plates (i.e. A = 1), and compare the numerical results of the LBE for hard-sphere molecules with those [12] of the Shakhov kinetic model equation [22], in Fig. 2(a).…”

Section: Analytical and Numerical Methodsmentioning

confidence: 99%

“…Note that to linearize the Boltzmann equation and various kinetic model equations (such as the Shakhov equation [22]), usually, the distribution function is expressed as f = f eq (1 + h 0 ), which makes the LBE elegant and calculation simple. Unfortunately, this kind of linearization does not allow the LBE to be solved numerically by the fast spectral method [23]; actually, the fast spectral method only works if we express the distribution function in the form of Eq.…”

Section: State Of the Problemmentioning

confidence: 99%

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Sound propagation through a rarefied gas in rectangular channels

2016

Phys. Rev. E

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This version is available at https://strathprints.strath.ac.uk/58309/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Sound propagation through a rarefied gas in rectangular channels A sound propagation through a rarefied gas inside a two-dimensional cavity is investigated on the basis of the linearized Boltzmann equation, where one of the cavity wall oscillates harmonically in the normal direction to its own surface and is considered as a sound source. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillation frequency on the average gas pressure exerted on the oscillating plate is studied. It is found that, at large values of the aspect ratio, the average pressure oscillates when the sound frequency varies, due to the sound resonance and anti-resonance along the oscillation direction of the plate. However, at small values of the aspect ratio, the average pressure is a monotonically decreasing function of the sound frequency, which cannot be observed in the corresponding one-dimensional counterpart. This is explained by the sound interference in the direction parallel to the oscillating plate. The influence of both the cavity aspect ratio and oscillation frequency on the sound speed is also investigated: again it is found that different aspect ratio leads to the different behavior of the sound speed as a function of the oscillation frequency.

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Section: Analytical and Numerical Methodsmentioning

confidence: 99%

Section: State Of the Problemmentioning

confidence: 99%

Sound propagation through a rarefied gas in rectangular channels

2016

Phys. Rev. E

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“…Its explicit form can be found in Ferziger and Kaper (1972), Cercignani (1975) and Sharipov and Seleznev (1998). Like our previous works (Sharipov and Kalempa, 2008b;Kalempa and Sharipov, 2009), here the Shakhov model (Shakhov, 1968;Sharipov and Seleznev, 1998) is employed. This model is the most appropriate to deal with the problem in question because it provides the correct Prandtl number, i.e.…”

Section: Input Equationmentioning

confidence: 98%

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Kalempa

Sharipov

2012

International Journal of Heat and Fluid Flow

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“…When b ¼ 0 the ES-BGK model reduces to the BGK model. In addition, Shakhov also proposed a so-called S-model to fix the Prandtl number issue [18,19], where the ''collision term'' can be written as @f @t…”

Section: The Es-bgk Modelmentioning

confidence: 99%

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

Meng

Reese

et al. 2013

Journal of Computational Physics

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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.

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Approximate kinetic equations in rarefied gas theory

Cited by 58 publications

References 7 publications

Sound propagation through a rarefied gas in rectangular channels

Sound propagation through a rarefied gas in rectangular channels

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

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

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