Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
520014 | Journal of Computational Physics | 2015 | 33 Pages |
Lately, there has been some interest in modifications of the compressible Navier–Stokes equations to include diffusion of mass. In this paper, we investigate possible ways to add mass diffusion to the 1-D Navier–Stokes equations without violating the basic entropy inequality. As a result, we recover Brenner's modification of the Navier–Stokes equations as a special case. We consider Brenner's system along with another modification where the viscous terms collapse to a Laplacian diffusion. For each of the two modifications, we derive a priori estimates for the PDE, sufficiently strong to admit a weak solution; we propose a numerical scheme and demonstrate that it satisfies the same a priori estimates. For both modifications, we then demonstrate that the numerical schemes generate solutions that converge to a weak solution (up to a subsequence) as the grid is refined.