Mathematics – Analysis of PDEs
Scientific paper
2005-03-11
Mathematics
Analysis of PDEs
15 pages. Submitted to the Proceedings of the Tenth International Conference on Hyperbolic Problems (HYP2004, held in Osaka, S
Scientific paper
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.
Liu Jian-Guo
Liu Jie
Pego Robert L.
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