Investigations of the Modified Navier-Stokes Equations in One Dimension
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In this thesis we have investigated the Brenner-Navier-Stoke equations in one spatial dimension. These are a modified version of the Navier-Stokes equations, where the modification relates to a mass diffusion term. This modification would be significant for flows with high density gradients. In this case we will examine a shock wave problem in Argon. Both the original and the modified Navier-Stokes equations will be used to solve the conservation laws. We will study the effect of both entropy-stable and entropy-conservative schemes, in addition to several several different ways to model the diffusion parameters. The solutions will be analyzed, and compared with experimental results.