I came across a text in Numerical Heat Tranfer by SV Patanakar that if we know the pressure field we don’t need to incorporate staggered grid arrangement. My question is: Don’t we require staggering of grid for velocity field in case of solving continuity equations? Even if we have the pressure field, we still need to solve for velocity etc.
Even though these may be thought to be treated as any other transport term in momentum equations but still we require velocities at faces e and w (going FV nomenclature) for calculating diffusion coefficients.
Won’t this create a problem as explained in scanned page in the attachment
Can someone comment regarding this?
Try going through the SMAC algorithm. In this we derive the pressure poisson equation, which require velocity at face centre value. But since we are solving for pressure in that equation, we do not need the grid to be staggered.
You can find the answer of your question in Andeson's book on CFD. Its very wel written.
You can see in Patankar book, topic The Pressure-Correction Equation in Chapter 6. It is the next step after Predictor step and is used for enforcing continutiy to get final corrected velocity field.
The velocity is required at faces, thats alright. Actually because of staggered grid approach our velocity is defined at faces only, so it becomes an advantage to use in Pressure correction Equation.
We have been taught this by our faculty in a very nice way based on FVM. The reference for it was Patnakar.
SMAC is not mentioned in patankar. The method you mentioned above is staggered grid approach I suppose.
I was asking reg SMAC
SMAC is a 1960's Algo (http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PFLDAS000008000012002182000001&idtype=cvips&doi=10.1063/1.1761178&prog=normal&bypassSSO=1)
And later SIMPLE Algo was the modfication of it over staggered grid.
w.r.t. your question, you can see the pressure-correction step in the SIMPLE algo. mentioned in Patankar.
Staggering was required ONLY if pressure was not known, because interpolation caused errors in computing pressure gradients(chequered board pressure distributions appeared numerically as..uniform pressure distributions, see book by Malalasekera,et. al).
However nowadays you can use collocated methods (no staggering) even when you solve for pressure. Each one has advantages and disadvantages.
Please see J.Papageorgakopoulos, et al, Enhancement of the momentum interpolation method on non-staggered grids, Int.J. for Numer.Meths.in fluids,33(1),pp1-22,2000.
Dear Sharma,
If the pressure is known, you have one variable less to compute, and you can drop one equation, which of them is left for discussion.
If you go ahead solving everything, one of the equation will have to enter as a constraint to the solution of the others, and you will have to look at the problem like a "constrained extrema", or something like this.
This will make you add another variable, a Lagrange limiter, to guarantee, lets say, the mass conservation. But this is exactly what pressure does, according to some people: it does correct the field of velocities to ensure mass conservation.
Let me ask you: are you working with fabricated solutions to check a code?
Best regards.
- Badges
- Science topic