Hi everybody, I am using a FV fractional step (Kim & Moin) method and a colocated grid approach but I have some problems related to the velocity correction. i solve the predictor step first and then I evaluate the fluxes at the the cells walls. Then I solve the Poisson equation for the pseudo-pressure and I correct the predictor velocity field. I correct separately the fluxes at the walls and the velocity at the cells centroids. While the correction for the fluxes is effective and the sum of the corrected fluxes at each cell is zero, if I recalculate the fluxes using the corrected velocities the sum is not null (this both if I use a QUICK or central scheme) The problem is that at the nexty time step I will use both fluxes and velocity to solve the momentum equations but the two fields are not consistent. Did anybody have the same problem ?
Re: Pressure correction
I have exactly the same problem. In fact, what happens, is that the flux field is divergence free, but the velocity field is not!! I quite don't know what to do about that, but at least my code is running and while comparing the results with a staggered mesh, it really looks the same. You may wanna take a look at the paper by: Y. Morinishi, T.S. Lund, O.V. Vasilyev, and P. Moin "Fully conservative Higher Order Finite Difference Schemes for incompressible flow". Journal of Comp. Phys., Vol 143, pp 90-124, 1998. (especially section 6 of this paper).
If you are working in general curvlinear coordinate, well i might have some questions for you!!
Re: Pressure correction
Everything is just fine: what happens here is characteristic for a collocated FVM: fluxes and velocities will be consistent only if the pressure variation is linear (unless you force it to be so). (Consistent means that the face interpolate of the velocity dotted with the face area vector equals the face flux).
Now you've got a choice:
1) you can put the additional term in the "velocity interpolation", equivalent to your Rhie-Chow treatment which will force consistency (I think it's in the Ferziger-Peric book; definitely in the Thesis by Samir Muzaferija and in some of his papers) and be happy
2) You can forget the whole thing: collocated FVM gives you effectively twice as many datum points for velocity (all faces + all cell centres) as for other cell-centred variables, so you can just as well benefit from this (useful for, say, LES).
I never bothered putting the correction in and the code is still stable, well behaved and gives the right behaviour with refinement (second-order).
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