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Howard Brenner has recently proposed modifications to the Navier-Stokesequations that relate to a diffusion of fluid volume that would be significantfor flows with high density gradients. In a previous paper (Greenshields &Reese, 2007), we found these modifications gave good predictions of the viscousstructure of shock waves in argon in the range Mach 1.0-12.0 (whileconventional Navier-Stokes equations are known to fail above about Mach 2).However, some areas of concern with this model were a somewhat arbitrary choiceof modelling coefficient, and potentially unphysical and unstable solutions. Inthis paper, we therefore present slightly different modifications to includemolecule mass diffusion fully in the Navier-Stokes equations. Thesemodifications are shown to be stable and produce physical solutions to theshock problem of a quality broadly similar to those from the family of extendedhydrodynamic models that includes the Burnett equations. The modificationsprimarily add a diffusion term to the mass conservation equation, so are atleast as simple to solve as the Navier-Stokes equations; there are none of thenumerical implementation problems of conventional extended hydrodynamicsmodels, particularly in respect of boundary conditions. We recommend furtherinvestigation and testing on a number of different benchmark non-equilibriumflow cases.

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