The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion

C.J. Greenshields, J.M. Reese

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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.
Original languageEnglish
Title of host publication2nd European Conference on Aero-Space Sciences (EUCASS)
Number of pages8
Publication statusPublished - Jul 2007
Event 2nd European Conference on AeroSpace Sciences (EUCASS), 2007 - Brussels, Belgium
Duration: 1 Jul 20076 Jul 2007


Conference 2nd European Conference on AeroSpace Sciences (EUCASS), 2007
Abbreviated titleEUCASS 2007


  • fluid dynamics
  • aerospace
  • structures
  • composites
  • design engineering

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