I am trying the solve the N-S incompressible equations with a pressure based method on a collocate grid with explicit time stepping. Can you tell me how to implement the Rhie Chow momentum interpolation for an explicit scheme?

I can't help with your basic question of implementing an explicit Rhie Chow scheme.

But I think that you meant 'colocated', not 'collocated'. 'Collocation' is (I think) a superposition solution technique.

Hi there,

The Rhie and Chow momentum interpolation is just a way of coupling the cell-center velocities (that do not conserve mass) with the pressure field. If you combine this approach with the fractional step method (explicit or semi-implicit), it has been shown to work very effectively. Anyway, the details of the implementation require some mathematical details that are well presented in the following paper: Morinishi, Lund, Vasilyev and Moin, Journal of Computational Physics, Vol 143, pp 90-124, 1998.( available online at: http://aero.uta.edu/~lund/ )

Now there are some deeper issues with the kinetic energy conservation associated with the interpolation operation itself and for this, take a look at the following paper:

Felten and Lund, Proceeding of 3rd AFOSR Int. Conf. DNS/LES, Arlington, Texas, Aug. 5-9 2001. (Available online at: http://aero.uta.edu/~felten/resume/resum.html )

This last paper has been reworked and enhanced since, and is about to be submitted to the J. Comp. Phys. A preprint will soon be available for download at the same address.

Sincerely,

Frederic Felten.

Thanks for your help. I shall look into these papers.