Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations

Taheri, Peyman; Torrilhon, Manuel; Struchtrup, Henning

doi:10.1063/1.3064123

Cited by 108 publications

(94 citation statements)

References 45 publications

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“…the flow direction is parallel to the plates. Due to the presence of this force, this Poiseuille flow is more interesting than Couette or Fourier flows, as it presents a bi-modal temperature profile that the NSF equations fail to predict even qualitatively [20,[23][24][25][26]. To assess the modeling accuracy of the ES-BGK equation, g x ¼ 0:22 and 1 (which are also close to the values used in previous BGK simulations [20] and DSMC simulations [23]) are chosen in the following simulations.…”

Section: Simulation Resultsmentioning

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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Section: Simulation Resultsmentioning

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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“…These terms are assumed to be zero in the Grad's formulation. The closure equations for these terms in the R13 formulation are (Taheri et al 2009): …”

Section: Derivation and Resultsmentioning

confidence: 99%

Higher-Order Continuum Equation Based Heat Conduction Law

Agrawal

2016

INAE Lett

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The Fourier law has the unphysical consequence of infinite speed of heat conduction. The Cattaneo modification to the heat conduction equation removes this deficiency. The modified equation however suffers from two main defects: the speed of propagation cannot be determined theoretically, and the equation can lead to results which violate the second law of thermodynamics. In this paper, we derive the Cattaneo equation starting from Grads 13-moment equations. Further, we derive a thermodynamically consistent conduction model from the regularized moment equations. The deficits in the existing models are therefore satisfactorily addressed in this work.

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“…The R13 equations have also shown good predictive capabilities in high-speed flows (Torrilhon & Struchtrup 2004). Only recently, a set of boundary conditions for the R13 equations has been provided (Struchtrup & Torrilhon 2007;, and it was shown that the equations can also predict Knudsen layer dominated problems to some extent Taheri et al 2009 solver. The error this introduces is acceptable for switching purposes, as an estimate of the local Knudsen number is sufficient.…”

Section: Local Knudsen Numbers Based On the R13 Equationsmentioning

confidence: 99%

Switching criteria for hybrid rarefied gas flow solvers

2009

Self Cite

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Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic near-equilibrium fluxes (i.e. the Navier-Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher order constitutive relations; in this case, we use the R13 equations. The efficacy of our proposed switching criteria is tested within an illustrative hybrid kinetic/Navier-Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

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Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations

Cited by 108 publications

References 45 publications

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

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

Higher-Order Continuum Equation Based Heat Conduction Law

Switching criteria for hybrid rarefied gas flow solvers

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