Stephen, There are two ways that I know of to deal with pressure checker boarding: staggered grids or some form of Rhie-Chow interpolation. IMO, these are simple only for uniform, Cartesian grids. For grids that are curvilinear, unstructured, non-uniform, and/or non-orthogonal, things get real complicated. There may be other methods, but something is required.
Regarding boundary conditions, I would suggest this text book: H. K. Versteeg and W. Malalasekera. An Introduction to Computational Fluid Dynamics, the Finite Volume Method. 2nd edition. Prentice-Hall. 2007 While this book uses the finite volume method, the explanation of boundary conditions and staggered grids is very good and relatively easy to interpret for finite difference. I would also recommend Joel H. Ferziger and Milovan Peric. Computational Methods for Fluid Dynamics. Springer-Verlag, 3rd edition, 2002. This is a little more general with regard to method discussing finite difference and finite volume, but still settling on finite volume. My $0.02: I question the use of finite difference. For Navier-Stokes, the use of finite volume is much more prevalent in commercial and research codes. If your student follows Versteeg and Malalasekera a simple, working, staggered grid FV code could be built in a very short time. If something more complicated is needed, it's probably explained in Ferziger and Peric. Also My $0.02: Unless the point of your student's work is to experience building her own code, why not download something like OpenFOAM (http://www.opencfd.co.uk/openfoam/) and just use it? I expect the effort to learn something like OpenFOAM for a simple application will be much less than writing a new code. Hope this helps. Bill >>>>> "Stephen" == Stephen Wornom <stephen.wornom at sophia.inria.fr> writes: Stephen> Shengyong wrote: >> Hi, Farshid >> >> Maybe she should use the staggered grid method which is very simple to >> implement. Stephen> Does it remain simple for curvilinear meshes? Stephen> Stephen >> >> On Tue, Aug 11, 2009 at 5:16 AM, Farshid Mossaiby <mossaiby at yahoo.com >> <mailto:mossaiby at yahoo.com>> wrote: >> >> Hi all, >> >> Sorry for this off-topic post. >> >> I am helping a master studnet which is working on solving >> Navier-Stokes equation with Finite Difference method. She is >> trying to eliminate spourious pressure modes from the solution. >> She needs to know some details that are not usually found in the >> papers but important when programming, e.g. boundary condition for >> pressure. If someone has expertise on this or know a *simple* FD >> code, I would be thankful to let me know. >> >> Best regards, >> Farshid Mossaiby >> >> >> >> >> >> >> -- >> Pang Shengyong >> Solidification Simulation Lab, >> State Key Lab of Mould & Die Technology, >> Huazhong Univ. of Sci. & Tech. China -- Bill Perkins Research Engineer Hydrology Group Pacific Northwest National Laboratory 902 Battelle Boulevard P.O. Box 999, MSIN K9-36 Richland, WA 99352 USA Tel: 509-372-6131 Fax: 509-372-6089 william.perkins at pnl.gov www.pnl.gov