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Howard Brenner has recently proposed modifications to the Navier-Stokes 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 1.0-12.0 (while conventional Navier-Stokes 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 Navier-Stokes 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 Navier-Stokes 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 non-equilibrium flow cases.
|Title of host publication||2nd European Conference on Aero-Space 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||2nd European Conference on AeroSpace Sciences (EUCASS), 2007|
|Abbreviated title||EUCASS 2007|
|Period||1/07/07 → 6/07/07|
- fluid dynamics
- design engineering
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- 2 Finished
1/11/07 → 31/10/10
1/09/04 → 30/09/07