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Abstract
Howard Brenner has recently proposed modifications to the NavierStokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.012.0 (while conventional NavierStokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the NavierStokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the NavierStokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark nonequilibrium flow cases.
Original language  English 

Title of host publication  2nd European Conference on AeroSpace Sciences (EUCASS) 
Number of pages  8 
Publication status  Published  Jul 2007 
Event  2nd European Conference on AeroSpace Sciences (EUCASS), 2007  Brussels, Belgium Duration: 1 Jul 2007 → 6 Jul 2007 
Conference
Conference  2nd European Conference on AeroSpace Sciences (EUCASS), 2007 

Abbreviated title  EUCASS 2007 
Country  Belgium 
City  Brussels 
Period  1/07/07 → 6/07/07 
Keywords
 fluid dynamics
 aerospace
 structures
 composites
 design engineering
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Dive into the research topics of 'The structure of hypersonic shock waves using NavierStokes equations modified to include mass diffusion'. Together they form a unique fingerprint.Projects
 2 Finished

Extended Continuum Models for Transient and Rarefied Hypersonic Aerothermodynamics
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/11/07 → 31/10/10
Project: Research

A HighOrder Continuum Model for Computational Hypersonic Aerodynamics
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/09/04 → 30/09/07
Project: Research