Moving boundary problems for a rarefied gas: Spatially one-dimensional case

Tsuji, Tetsuro; Aoki, Kazuo

doi:10.1016/j.jcp.2013.05.017

Cited by 37 publications

(48 citation statements)

References 24 publications

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“…In addition, it is known that the variation of f is steep for the molecular velocities in the vicinity of the discontinuities, so that we have to use a grid system for ζ 1 that concentrates in the neighborhood of the discontinuities. The reader is referred to [7] for the details of the numerical method, including the treatment of singularities weaker than the discontinuities.…”

Section: Methodsmentioning

confidence: 99%

“…The characteristic line tangent to the trajectory of the plate and the discontinuity [7]. (a) The case where the characteristic line meets the trajectory, (b) the case where the characteristic line does not meet the trajectory.…”

Section: Figmentioning

confidence: 99%

“…o VI, [1][2][3][4][5][6][7][8][9][10][11][12][13] VI-1 on the gas molecules. However, if the planar boundary is moving with acceleration/deceleration in its normal direction (for example, an oscillatory motion), the discontinuity on the boundary in general propagates into the gas.…”

Section: Introductionmentioning

confidence: 99%

“…We describe the singularities in the velocity distribution function caused by the motion of the boundary and give an outline of the numerical method that captures the singularity. The notes are based on the authors' recent works [6,7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems

Aoki¹,

Tsuji²

2014

Séminaire Laurent Schwartz — EDP Et Applications

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Section: Methodsmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems

Aoki¹,

Tsuji²

2014

Séminaire Laurent Schwartz — EDP Et Applications

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“…Consequently, the system response was always assumed time-periodic, and only the space variation of flowfield properties has been considered. In a recent contribution, Tsuji and Aoki [10] have considered a nonlinear timedependent problem of a passive plate-on-a-spring setup interacting with a semi-infinite gas expanse. As this is the only occasion where time-dependent acoustic equilibration has been investigated, much work is still required to analyze the approach to acoustic relaxation in a rarefied medium.…”

Section: Introductionmentioning

confidence: 99%

The response of a confined rarefied gas to non-periodic acoustic excitation

Manela¹,

Oskar²

2014

AIP Conference Proceedings

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The response of a gas, confined in a microchannel and subject to to instantaneous (small-amplitude) motion of its boundaries in the normal direction, is considered. The problem is formulated using the Bhatnagar, Gross and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers, combining analytical (collisionless and continuum-limit) solutions with numerical (linearized BGK) calculations. In difference from most existing studies, the case of non-periodic boundary actuation and system approach to equilibrium is investigated. Gas rarefaction is shown to have a "damping effect" on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuum-limit solution, however, should be considered with care at early times near the location of acoustic wavefronts,

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Immersed boundary method for unsteady kinetic model equations

Pekardan

Chigullapalli

Sun³

et al. 2015

Numerical Methods in Fluids

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Summary Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.

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Moving boundary problems for a rarefied gas: Spatially one-dimensional case

Cited by 37 publications

References 24 publications

Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems

Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems

The response of a confined rarefied gas to non-periodic acoustic excitation

Immersed boundary method for unsteady kinetic model equations

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