DMCA
An overview of projection methods for incompressible flows
Cached
Download Links
| Venue: | Comput. Methods Appl. Mech. Engrg |
| Citations: | 203 - 21 self |
BibTeX
@ARTICLE{Guermond_anoverview,
author = {J. L. Guermond and Jie Shen},
title = {An overview of projection methods for incompressible flows},
journal = {Comput. Methods Appl. Mech. Engrg},
year = {},
volume = {41},
pages = {112--134}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. We introduce and study a new class of projection methods—namely, the velocitycorrection methods in standard form and in rotational form—for solving the unsteady incompressible Navier–Stokes equations. We show that the rotational form provides improved error estimates in terms of the H 1-norm for the velocity and of the L 2-norm for the pressure. We also show that the class of fractional-step methods introduced in [S. A. Orsag, M. Israeli, and M. Deville, J. Sci. Comput., 1 (1986), pp. 75–111] and [K. E. Karniadakis, M. Israeli, and S. A. Orsag, J. Comput. Phys., 97 (1991), pp. 414–443] can be interpreted as the rotational form of our velocity-correction methods. Thus, to the best of our knowledge, our results provide the first rigorous proof of stability and convergence of the methods in those papers. We also emphasize that, contrary to those of the above groups, our formulations are set in the standard L 2 setting, and consequently they can be easily implemented by means of any variational approximation techniques, in particular the finite element methods. Key words. Navier–Stokes equations, projection methods, fractional-step methods, incompressibility, finite elements, spectral approximations
Keyphrases
projection method rotational form incompressible flow fractional-step method navier stokes equation spectral approximation improved error estimate new class first rigorous proof key word variational approximation technique finite element finite element method velocity-correction method unsteady incompressible navier stokes equation standard form velocitycorrection method
