Weak solutions and convergent numerical schemes of modified compressible Navier-Stokes equations

作者：Svard Magnus^*

来源：Journal of Computational Physics, 2015, 288: 19-51.

DOI：10.1016/j.jcp.2015.02.013

• Conservation laws
• Modified Navier-Stokes equations
• Convergence
• Weak solutions
• Finite difference

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.

• 出版日期2015-5-1