Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries

Creators: Hou, Thomas Y.; Wetton, Brian T. R.

Abstract

A rigorous convergence result is given for a projection scheme for the Navies–Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition. This choice for the pressure and the particular way that the discrete divergence is calculated near the boundary permit the error in the pressure to be controlled and the second-order convergence in the velocity and the pressure to the exact solution to be shown. Some simplifications in the calculation of the pressure in the case without boundaries are also discussed.

Additional Information

© 1993 Society for Industrial and Applied Mathematics. Received by the editors April 29, 1991; accepted for publication (in revised form) June 2, 1992. This research was supported in part by Air Force Office of Scientific Research grant AFOSR-90-0090. The work of this author [T.Y.H.] was supported by National Science Foundation grant DMS-9003202 and by a Sloan foundation fellowship. The work of this author [B.T.R.W.] was supported by Natural Sciences and Engineering Research Council grant OGP0122105. We thank Professor Chris Anderson for bringing this problem to our attention and for several beneficial discussions. We also thank the reviewers, Christoph Borgers and Luis Reyna, for many insightful comments.

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