# On the PIMPLE algorithm

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 October 4, 2010, 09:17 On the PIMPLE algorithm #1 Senior Member   Vesselin Krastev Join Date: Jan 2010 Location: University of Tor Vergata, Rome Posts: 368 Rep Power: 20 Hi all, can someone give me some brief explanation (or at least some bibliografical reference) about how the PIMPLE algorithm works (namely how the "merging" between the PISO and SIMPLE algorithms is accomplished)? Thank you in advance V.

 October 4, 2010, 10:40 #2 Senior Member   Vesselin Krastev Join Date: Jan 2010 Location: University of Tor Vergata, Rome Posts: 368 Rep Power: 20 Any replies?

 April 16, 2012, 09:12 #3 New Member   Gilles De Neyer Join Date: Nov 2011 Posts: 18 Rep Power: 14 Hello, Did you get some informations about this ? I'm also interested in the way Pimple algorithm works, especially for compressible flow ! Is there a paper speaking about this ? Thank you, Gilles

April 16, 2012, 09:42
#4
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Vesselin Krastev
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 Originally Posted by gdeneyer Hello, Did you get some informations about this ? I'm also interested in the way Pimple algorithm works, especially for compressible flow ! Is there a paper speaking about this ? Thank you, Gilles
Well, actually the PIMPLE algorithm is nothing but a PISO procedure with two (eventual) additions: 1) outer correction loops (i. e. multiple cycling over the same time step using the last iteration final value as initial guess for the next iteration); 2) underrelaxation of the variables between consequent outer iterarions.

So, to better understand the algorithm, I suggest you to get familiar (if you are still not) with pressure-correction algorithms (a good reading about this should be Patankar's book "Numerical Heat Transfer and Fluid Flow") and after that to focus on the PISO one (it is described in many CFD books, but my advice is to start from Issa's original paper "Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting", which should be freely available in the open literature)

Hope this helps

V.

 April 16, 2012, 10:14 #5 New Member   Gilles De Neyer Join Date: Nov 2011 Posts: 18 Rep Power: 14 thank you for your answer, I've already read several docs about PISO algorithm in which the Phd thesis of Professor Jasak and the Jerziger. I think I know understand well this procedure. What concerns me is that the PISO algorithm uses the continuity equation to compute an equation for pressure and I don't know exactly how this apply for compressible flows (as in rhoPimpleFoam) as the continuity equation involve rho and the energy equation is now coupled to the others.

April 16, 2012, 10:54
#6
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Vesselin Krastev
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Location: University of Tor Vergata, Rome
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Quote:
 Originally Posted by gdeneyer thank you for your answer, I've already read several docs about PISO algorithm in which the Phd thesis of Professor Jasak and the Jerziger. I think I know understand well this procedure. What concerns me is that the PISO algorithm uses the continuity equation to compute an equation for pressure and I don't know exactly how this apply for compressible flows (as in rhoPimpleFoam) as the continuity equation involve rho and the energy equation is now coupled to the others.
For low-Mach number flows (e.g. low speed flows, but with significant compressibility due to heat transfer) the compressible PISO/SIMPLE algorithms work exactly as the incompressible ones: you couple pressure and velocity (pressure correction equation is again derived from continuity, starting from a guessed density field usually linked to the initial pressure and temperature fields through the equation of state), you solve the energy equation then you update the density field through the equation of state (and eventually solve the turbulence equations), repeating the whole loop till convergence. If the flow Mach number approaches (or goes beyond) Mach=1, then a modification on the pressure correction equation is needed (see for instance "A COLLOCATED FINITE VOLUME METHOD FOR PREDICTING FLOWS AT ALL SPEEDS", from Demirdzitc et al.), but the concept behind the algorithm remains the same.

Regards

V.

 April 16, 2012, 10:59 #7 New Member   Gilles De Neyer Join Date: Nov 2011 Posts: 18 Rep Power: 14 thank you again Mr Vesselin Krastev, I understand the methodology even if it is unclear to me how we should decide the order of processing the equations (velocity, energy, pressure, ...) I m gonna look deeper in the implementation of rhoPimpleFoam for details.

April 16, 2012, 11:13
#8
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Vesselin Krastev
Join Date: Jan 2010
Location: University of Tor Vergata, Rome
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Quote:
 Originally Posted by gdeneyer thank you again Mr Vesselin Krastev, I understand the methodology even if it is unclear to me how we should decide the order of processing the equations (velocity, energy, pressure, ...) I m gonna look deeper in the implementation of rhoPimpleFoam for details.
If you take a careful look on the two references I mentioned I think that everything will be more clear.

Regards

V.