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Fundamental solutions to the R13 equations : efficient computation of 3D kinetic effects

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Claydon, Rory, Shrestha, Abhay, Rana, Anirudh Singh, Sprittles, James E. and Lockerby, Duncan A. (2017) Fundamental solutions to the R13 equations : efficient computation of 3D kinetic effects. Journal of Fluid Mechanics, 833 . R4. doi:10.1017/jfm.2017.763 ISSN 0022-1120.

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Official URL: https://doi.org/10.1017/jfm.2017.763

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Abstract

Fundamental solutions (Green’s functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier–Stokes–Fourier equations). Incorporation of these new fundamental solutions into a numerical framework based on the method of fundamental solutions (MFS) allows for efficient computation of three-dimensional gas microflows at remarkably low computational cost. The R13-MFS approach accurately recovers analytic solutions for low-speed flow around a stationary sphere and heat transfer from a hot sphere (for which a new analytic solution has been derived), capturing non-equilibrium flow phenomena missing from lower-order solutions. To demonstrate the potential of the new approach, the influence of kinetic effects on the hydrodynamic interaction between approaching solid microparticles is calculated. Finally, a programme of future work based on the initial steps taken in this article is outlined.

Item Type: Journal Article
Subjects: Q Science > QC Physics
T Technology > TJ Mechanical engineering and machinery
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Gas flow, Gas dynamics, Nanofluids, Kinetic theory of gases, Rarefied gas dynamics, Fluid dynamics
Journal or Publication Title: Journal of Fluid Mechanics
Publisher: Cambridge University Press
ISSN: 0022-1120
Official Date: 25 December 2017
Dates:
DateEvent
25 December 2017Published
8 November 2017Available
1 October 2017Accepted
Volume: 833
Article Number: R4
DOI: 10.1017/jfm.2017.763
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 16 October 2017
Date of first compliant Open Access: 28 March 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N016602/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/P020887/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/K038664/1 [EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/P031684/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDLeverhulme Trusthttp://dx.doi.org/10.13039/501100000275
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