On Incompressible Navier-Stokes Dynamics: A New Approach for Analysis and Computation
Abstract
We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as a perturbed vector diffusion equation, instead of as a perturbed Stokes system. To illustrate the advantages of this view, we provide a simple proof of the unconditional stability of a difference scheme that is implicit only in viscosity and explicit in both pressure and convection terms, requiring no solution of stationary Stokes systems or inf-sup conditions.
Keywords
Cite
@article{arxiv.math/0503212,
title = {On Incompressible Navier-Stokes Dynamics: A New Approach for Analysis and Computation},
author = {Jian-Guo Liu and Jie Liu and Robert L. Pego},
journal= {arXiv preprint arXiv:math/0503212},
year = {2007}
}
Comments
15 pages. Submitted to the Proceedings of the Tenth International Conference on Hyperbolic Problems (HYP2004, held in Osaka, September 2004), Yokohama Publishers, Inc