A kinetic theory solution method for the Navier-Stokes equations

Macrossan, M. N. and Oliver, R. I. (1993) A kinetic theory solution method for the Navier-Stokes equations. International Journal for Numerical Methods in Fluids, 17 3: 177-193. doi:10.1002/fld.1650170302

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Author Macrossan, M. N.
Oliver, R. I.
Title A kinetic theory solution method for the Navier-Stokes equations
Journal name International Journal for Numerical Methods in Fluids   Check publisher's open access policy
ISSN 0271-2091
Publication date 1993-01-01
Sub-type Article (original research)
DOI 10.1002/fld.1650170302
Open Access Status File (Author Post-print)
Volume 17
Issue 3
Start page 177
End page 193
Total pages 17
Language eng
Subject 240502 Fluid Physics
Abstract The kinetic-theory-based solution methods for the Euler equations proposed by Pullin and Reitz are here extended to provide new finite volume numerical methods for the solution of the unsteady Navier-Stokes equations. Two approaches have been taken. In the first, the equilibrium interface method (EIM), the forward- and backward-flowing molecular fluxes between two cells are assumed to come into kinetic equilibrium at the interface between the cells. Once the resulting equilibrium states at all cell interfaces are known, the evaluation of the Navier-Stokes fluxes is straightforward. In the second method, standard kinetic theory is used to evaluate the artificial dissipation terms which appear in Pullin's Euler solver. These terms are subtracted from the fluxes and the Navier-Stokes dissipative fluxes are added in. The new methods have been tested in a 1D steady flow to yield a solution for the interior structure of a shock wave and in a 2D unsteady boundary layer flow. The 1D solutions are shown to be remarkably accurate for cell sizes large compared to the length scale of the gradients in the flow and to converge to the exact solutions as the cell size is decreased. The steady-state solutions obtained with EIM agree with those of other methods, yet require a considerably reduced computational effort.
Keyword viscous flow
kinetic theory
finite volume method
equilibrium interface method
equilibrium flux method
Euler equations
Navier-Stokes equations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown
Additional Notes This is an author version of an article originally published as Macrossan, M. N. and Oliver, R. I. (1993) A kinetic theory solution method for the Navier-Stokes equations, International Journal for Numerical Methods in Fluids 17 (3) : 177-193. doi: 10.1002/fld.1650170302 Copyright John Wiley & Sons 1993. All rights reserved.

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mechanical & Mining Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 17 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 20 times in Scopus Article | Citations
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Created: Wed, 20 Dec 2006, 09:34:56 EST by Michael N Macrossan