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steadystate PISO's corrector step

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Old   July 5, 2013, 03:41
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Dongyue Li
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Hi,

In SIMPLE and steadystate PISO, There are a little differences, and I made a picture to show this by my comprehension. What I am courious about is why there are some correctors loops in PISO, in my image, if I get u** v** p**, it has been divergence free, But if omit this correctors loop, PISO would become SIMPLE ....

So whats the meaning of this correctors loop in steadystate PISO?

Just now I compiled a steadyStatePisoFoam, use this solver solving cavity it use 317 iterations compared with simpleFoam's 47's iterations. So now I am more confused about this inner loop, can it really speed up the solving process?

And in Versteeg's book page 196, he said:"As before, under-relaxation is required with the procedure in PISO" , AFAIK, in openFoam PISO dont need relaxation. so??
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Last edited by sharonyue; July 9, 2013 at 19:53.
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Old   July 5, 2013, 07:51
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Mohsen KiaMansouri
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Somebody please compare the SIMPLE, PISO and PIMPLE loops in a single flowchart.
I'm confused too
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Old   July 7, 2013, 19:58
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Still confused too
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Old   July 8, 2013, 05:48
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Looks like steadystate PISO is different with transient PISO. In this thread http://www.chemical-forum.com/thread-71382-1-1.html He said:
Code:
Hi,
The original version of PISO was developed for transient calculation with small timesteps, so you have also small Courant numbers (<1) in this non-iterative variant. If you are running PISO like SIMPLE with outer Iterations you do not need small Courant numbers, but the convergence rate of PISO will then not be better or faster than SIMPLE! See also the paper "Solution of the implicitly discretised fluid flow euqations by operator splitting" by R.I. Issa!
Good Luck!
This maybe what Ive encounterd. But back to Versteeg's book page 196, Thats contradictory!!

And, does it mean the momentum and continuity equations are simultaneously satisfied after the inner loops in PISO?
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Old   July 9, 2013, 11:18
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Hi Forrest,
In OpenFOAM there is no PISO algorithm for steady-state simulation, only for transient flow simulations. You can use it to solve a steady state problem if you let the simulation continue for such a long time that the transient behavior disappears, but there are some flows that never reach this condition, like the flow around a cylinder that has vortex shedding behavior. For a real steady flow simulation you can use SIMPLE. The PISO algorithm has a limitation that the time step must be small otherwise it will diverge so, to overcome this limitation the PIMPLE algorithm was developed, it is a combination of the two algorithms.
Best Regards,
Paulo

Last edited by vatavuk; July 9, 2013 at 11:23. Reason: make it more clear
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Old   July 9, 2013, 20:04
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Quote:
Originally Posted by vatavuk View Post
Hi Forrest,
In OpenFOAM there is no PISO algorithm for steady-state simulation, only for transient flow simulations. You can use it to solve a steady state problem if you let the simulation continue for such a long time that the transient behavior disappears, but there are some flows that never reach this condition, like the flow around a cylinder that has vortex shedding behavior. For a real steady flow simulation you can use SIMPLE. The PISO algorithm has a limitation that the time step must be small otherwise it will diverge so, to overcome this limitation the PIMPLE algorithm was developed, it is a combination of the two algorithms.
Best Regards,
Paulo
But PISO can deal with the steady state, what Im confused about is this steady state PISO's algorithm, I dont know why there is corrector step 2, its have been divergence free in corrector step 1.
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