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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
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 | ||||||||||||||||||
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| Subjects: | Q Science > QC Physics T Technology > TJ Mechanical engineering and machinery |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| 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 | ||||||||||||||||||
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| 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: |
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