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Title of Journal: Continuum Mech Thermodyn

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Abbravation: Continuum Mechanics and Thermodynamics

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Springer-Verlag

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DOI

10.1002/crat.200800363

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1432-0959

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A phenomenological and extended continuum approach

Authors: S Mizzi R W Barber D R Emerson J M Reese S K Stefanov
Publish Date: 2007/07/31
Volume: 19, Issue: 5, Pages: 273-283
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Abstract

This paper presents a new technique that combines Grad’s 13moment equations G13 with a phenomenological approach to rarefied gas flows This combination and the proposed solution technique capture some important nonequilibrium phenomena that appear in the early continuumtransition flow regime In contrast to the fully coupled 13moment equation set a significant advantage of the present solution technique is that it does not require extra boundary conditions explicitly Grad’s equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport The relative computational cost of this novel technique is low in comparison to other methods such as fully coupled solutions involving many moments or discrete methods In this study the proposed numerical procedure is tested on a planar Couette flow case and the results are compared to predictions obtained from the direct simulation Monte Carlo method This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from nonequilibrium phenomena which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications


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