Abstract
A modified projection method is proposed for the long-term computation of Navier-Stokes equations. The idea is to add to the pressure a “damping” mechanism to prevent it from overshooting. A discrete analogue of the energy inequality enjoyed by the original system is established and local error estimations are presented. Numerical experiments and comparisons for different versions of the projection method are reported.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chorin, A. (1968). Numerical simulation of the Navier-Stokes equations.Math. of Comput. 22, 745–762.
Girault, V., and Raviart, P. A. (1986).Finite Element Methods for Navier-Stokes Equations, Springer-Verlag.
Goda, K. (1979). A multistep technique with implicit difference scheme for evaluating two- or three-dimensional cavity flows.J. Comput. Phys. 30, 76–95.
Guermond, J.-L. (1994). Some error estimates for the approximation of the unsteady Navier-Stokes equations by means of projection methods, (Preprint).
Kim, J., and Moin, P. Application of a fractional-step method to incompressible Navier-Stokes equations.J. Comput. Phys. 59, 308–323.
Kovasznay, L. I. G. (1948). Laminar flow behind two-dimensional grid.Proc. Cambridge Philos. Soc. 44, 58–62.
Quarteroni, A., and Valli, A. (1994).Numerical Approximation of Partial Differential Equations, Springer-Verlag.
Shen, J. (1992). On error estimates of the projection method for the Navier-Stokes equations, first order scheme.SIAM J. Numer. Anal. 29, 57–71.
Shen, J. (1994). Remarks on the pressure error estimates for the projection methods.Numer. Math. 67, 513–520.
Simo, J. C., and Armero, F. (1994). Unconditional stability and long-term behavior of transient algorithm for the incompressible Navier-Stokes and Euler equations.Comput. Meth. in Appl. Mech. & Engin. 111, 111–154.
Temam, R. (1968). Une Méthode d'approximations de la solution des équations de Navier-Stokes.Bull. Soc. Math. France 98, 115–152.
Temam, R. (1988). Infinite dimensional dynamical systems in mechanics and physics,Applied Mathematical Sciences, Vol. 68, Springer-Verlag.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cao, WM., Carlenzoli, C. A projection method for long-term computation of Navier-Stokes equations. J Sci Comput 11, 373–395 (1996). https://doi.org/10.1007/BF02088953
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02088953