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Abstract
We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a meanfreevolume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display nonlocalthermodynamicequilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.
Original language  English 

Pages (fromto)  60796094 
Number of pages  16 
Journal  Physica A: Statistical Mechanics and its Applications 
Volume  387 
Issue number  24 
DOIs  
Publication status  Published  15 Oct 2008 
Keywords
 gas kinetic theory
 Boltzmann equation
 compressible fluids
 NavierStokes equations
 rarefied gas dynamics
 constitutive relations
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 1 Finished

BEYOND NAVIERSTOKES: MEETING THE CHALLENGE OF NONEQUILIBRIUM GAS DYNAMICS
Reese, J. & McInnes, C.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/05 → 31/01/10
Project: Research