Fractional step methods for the Navier-Stokes equations on non-staggered grids.
by
Steve Armfield
Sydney University.
Coauthors: Bob Street (Stanford University)

Time integration of the Navier-Stokes equations is often carried out by means of the fractional-step procedure. At each time step an incomplete form of the momentum equations is integrated to yield an approximate velocity field, which will in general not be divergence free, then a correction is applied to that velocity field to produce a divergence free velocity field. The correction to the velocity field is an orthogonal projection in the sense that it projects the initial velocity field onto the divergence free field without changing the vorticity. It has been shown that second order in time projection methods may be constructed for staggered mesh schemes. When these methods are applied to non-staggered schemes the interaction between the pressure gradient terms and continuity can result in a first order in time error, independent of the time accuracy of the momentum equations. The application and accuracy of fractional step methods on non-staggered grids will be presented and discussed and results presented demonstrating the behaviour of the schemes for unsteady cavity flow. A scheme with second order in time accuracy will be proposed.

Date received: August 2, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-98.