Macroscopic transport models for rarefied gas flows: a brief review

Struchtrup, Henning; Taheri, Peyman

doi:10.1093/imamat/hxr004

Cited by 75 publications

(56 citation statements)

References 87 publications

(195 reference statements)

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“…Nevertheless, Grad's method has one major drawback: unlike the Chapman-Enskog expansion it lacks a small parameter, such as the Knudsen number, in which one can do power-counting and thus systematically improve the approximation [11]. This deficiency, together with the bad performance of Grad's method in comparison to microscopic calculations [12], have led researchers to abandon this approach for some time.…”

Section: Introductionmentioning

confidence: 99%

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

et al. 2012

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In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.

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Section: Introductionmentioning

confidence: 99%

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

et al. 2012

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“…It is a purely non-equilibrium effect caused by the Knudsen layer. The non-uniform pressure has been observed in molecular dynamics (MD) simulations (Holyst & Litniewski 2008;Cheng et al 2011;, kinetic theory computations (Sone & Onishi 1978) and previous works Struchtrup & Taheri 2011) for different flow configurations. Evidently, the NSF equations fail to capture this phenomenon.…”

Section: Solution To the R13 Equationsmentioning

confidence: 95%

Evaporation-driven vapour microflows: analytical solutions from moment methods

2018

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Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier-Stokes-Fourier, regularised 13-moment and regularised 26-moment frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number 1, whilst providing clear insight into non-equilibrium phenomena occurring adjacent to the interface.

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“…In the R13 equations, stress σ i j and heat flux q k are considered as flow variables with their own balance equations, which read for Maxwell molecules, 5,9,21,31 Dσ i j Dt + 4 5…”

Section: A R13 Equationsmentioning

confidence: 99%

Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

Rana

Struchtrup

2015

Physics of Fluids

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The driven cavity flow over the whole range of the Knudsen number Phys. The velocity dependent Maxwell (VDM) model for the boundary condition of a rarefied gas, recently presented by Struchtrup ["Maxwell boundary condition and velocity dependent accommodation coefficient," Phys. Fluids 25, 112001 (2013)], provides the opportunity to control the strength of the thermal transpiration force at a wall with temperature gradient. Molecular simulations of a heated cavity with varying parameters show intricate flow patterns for weak, or inverted transpiration force. Microscopic and macroscopic transport equations for rarefied gases are solved to study the flow patterns and identify the main driving forces for the flow. It turns out that the patterns arise from a competition between thermal transpiration force at the boundary and thermal stresses in the bulk. C 2015 AIP Publishing LLC.

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Macroscopic transport models for rarefied gas flows: a brief review

Cited by 75 publications

References 87 publications

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

Evaporation-driven vapour microflows: analytical solutions from moment methods

Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

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