A Note on the Propagation of Boundary Induced Discontinuities in Kinetic Theory

Aoki, Kazuo; Bardos, Claude; Dogbe, Christian; Golse, François

doi:10.1142/s0218202501001483

Cited by 28 publications

(44 citation statements)

References 14 publications

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“…The paper by Cercignani (2000) should also be mentioned as a related work. A mathematical study of the propagation of boundaryinduced discontinuities in the solution of a simple kinetic equation is found in Aoki et al (2001a). Also, quite recently a mathematical description of the formation and propagation of a discontinuity (in a gas in a non-convex domain) was given for the solution of the Boltzmann equation by Kim (2011).…”

Section: Discontinuity In the Velocity Distribution Functionmentioning

confidence: 99%

Rarefied gas flow around a sharp edge induced by a temperature field

Taguchi

Aoki

2012

J. Fluid Mech.

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A rarefied gas flow thermally induced around a heated (or cooled) flat plate, contained in a vessel, is considered in two different situations: (i) both sides of the plate are simultaneously and uniformly heated (or cooled); and (ii) only one side of the plate is uniformly heated. The former is known as the thermal edge flow and the latter, typically observed in the Crookes radiometer, may be called the radiometric flow. The steady behaviour of the gas induced in the container is investigated on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The flow features are clarified for a wide range of the Knudsen number, with a particular emphasis placed on the structural similarity between the two flows. The limiting behaviour of the flow as the Knudsen number tends to zero (and thus the system approaches the continuum limit) is investigated for both flows. The detailed structure of the normal stress on the plate as well as the cause of the radiometric force (the force acting on the plate from the hotter to the colder side) is also clarified for the present infinitely thin plate.

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Section: Discontinuity In the Velocity Distribution Functionmentioning

confidence: 99%

Rarefied gas flow around a sharp edge induced by a temperature field

Taguchi

Aoki

2012

J. Fluid Mech.

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“…Although, methodologies have been proposed to eliminate this problem [15,16], it is obvious that the development and implementation of alternative computational schemes, which are not subject to ray effects, will be very useful. This need is also justified by the increased interest during the last years of solving rarefied gas flows in several emerging engineering and technological fields [17].…”

Section: Introductionmentioning

confidence: 99%

Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

Varoutis

Valougeorgis

Sharipov

2008

Journal of Computational Physics

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“…Again the discontinuous behavior of the fmf case is smoothed for a great but finite Kn value. The two-dimensional reduced distribution function is reported as was done in and for comparison with Aoki et al 13 At this point we conclude by presenting the final results for the thermal problem. In particular Table II reports the data concerning the thermodynamic temperature th ϭT th /T 1 and the kinetic temperature k ϭT k /T 1 , and their difference ⌬ϭ th Ϫ k for two values of w and three values of Kn.…”

Section: Resultsmentioning

confidence: 84%

The velocity distribution function in direct simulation Monte Carlo method with an application to extended thermodynamics

Marino

2003

Physics of Fluids

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A numerical experiment is carried out to prove the difference between the value of the kinetic temperature and that of the thermodynamic temperature in a gas in the presence of molecular transport. As a reference situation the velocity distribution function is evaluated between two concentric cylinders at different wall temperatures. A direct simulation Monte Carlo method (DSMC) is adopted for various Knudsen numbers Kn and comparisons are made with existing data. The results prove quantitatively that the difference between the two differently defined temperatures increases with Kn and with the temperature gradient, as predicted by the theory for systems which are almost in thermodynamical equilibrium. The present article does not aim to validate DSMC, but rather to illustrate how the method can be used to address fundamental issues in gas dynamics.

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A Note on the Propagation of Boundary Induced Discontinuities in Kinetic Theory

Cited by 28 publications

References 14 publications

Rarefied gas flow around a sharp edge induced by a temperature field

Rarefied gas flow around a sharp edge induced by a temperature field

Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

The velocity distribution function in direct simulation Monte Carlo method with an application to extended thermodynamics

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