A concise and accurate solution for Poiseuille flow in a plane channel

Siewert, C. E.; Garcia, R. D. M.; Grandjean, P.

doi:10.1063/1.524396

Cited by 28 publications

(12 citation statements)

References 11 publications

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“…[9] and [10] for the various problems we have solved here, and we have confirmed precisely the Poiseuille-flow results from Ref. [23]. In addition, we have increased the value of N used in our computations until we found stability in the final results.…”

Section: Numerical Resultssupporting

confidence: 66%

Unified solutions to classical flow problems based on the BGK model

Barichello

Camargo

Rodrigues

et al. 2001

Z. angew. Math. Phys.

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A version of the discrete-ordinates method is used to solve in a unified manner some classical flow problems based on the Bhatnagar, Gross and Krook model in the theory of rarefiedgas dynamics. In particular, the thermal-creep problem and the viscous-slip (Kramers') problem are solved for the case of a semi-infinite medium, and the Poiseuille-flow problem, the Couetteflow problem and the thermal-creep problem are all solved for a wide range of the Knudsen number.

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Section: Numerical Resultssupporting

confidence: 66%

Unified solutions to classical flow problems based on the BGK model

Barichello

Camargo

Rodrigues

et al. 2001

Z. angew. Math. Phys.

Self Cite

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“…An alternative form for the flow rate can be obtained by following the projection procedure outlined in [5] in terms of the outgoing surface perturbation:…”

Section: Formulation Of the Dvm Equationsmentioning

confidence: 99%

“…A second set of benchmarks can be found in [5]. These results are for no accommodation at the surfaces (α = 1) and a wide variety of channel widths.…”

Section: The Flow Ratementioning

confidence: 99%

“…In particular, for flow of a rarefied gas down a channel resulting from a pressure gradient, called Poiseuille flow, various numerical formulations exist [1][2][3][4][5][6][7]. With the development of fast linear algebra solvers as well as fast computational platforms, one contemporary method stands out among all those previously developed.…”

Section: Introductionmentioning

confidence: 99%

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Mining the discrete velocity method for high quality solutions for one-dimensional Poiseuille flow

Ganapol

2006

Z. angew. Math. Phys.

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A fully discretized solution for Poiseuille flow in a one-dimensional channel is presented. Unlike previous semi-analytical methods, such as the Analytical Discrete-Ordinates (ADO) or the FN methods, which have been specifically designed to avoid spatial discretization error, no analytical advantage is assumed. Instead, the solution is "mined" in a process where each discrete approximation is an element in a sequence of solutions whose convergence to the solution is accelerated. This process leads most straightforwardly to high quality benchmark results for use in algorithm verification with a minimum of theoretical and numerical complexity.

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“…The reader is referred to [1][2][3][4][5][6], and other references therein for an overview of the recent work in this area. Earlier researches [7][8][9][10][11][12] solved rarefied gas dynamics problems using different methods. It has been shown that these methods yield good results.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

Njoseh¹,

Musa²

2013

JAMP

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A comparison of two methods of solution to classical flow problem in rarefied gas dynamics was presented. The two methods were chosen to examine the effect of the following transport phenomena (pressure gradient and temperature difference) viz Poiseuille and Thermal creep respectively on the flow of rarefied gas. The governing equations were approximated using BGK model. It was shown that while the Discrete Ordinate Method could consider more values of the accommodation coefficients, the Finite Difference Method can only take accommodation coefficient of one. It was also shown that the flow rate has its minimum in both solution methods at K n = 0.1 in the transition regime and that as the channels get wider, the Thermal creep volume flow rates get smaller.

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A concise and accurate solution for Poiseuille flow in a plane channel

Cited by 28 publications

References 11 publications

Unified solutions to classical flow problems based on the BGK model

Unified solutions to classical flow problems based on the BGK model

Mining the discrete velocity method for high quality solutions for one-dimensional Poiseuille flow

Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

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