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May 30, 2015, 11:21 
The spirit of SIMPLE algorithm in simpleFoam

#1 
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Dongyue Li
Join Date: Jun 2012
Location: Torino, Italy
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Hello guys!
Im wondering where is the sprit of SIMPLE algorithm in simpleFoam. As we know in staggered mesh, the key point of SIMPLE is that: But I did not see this is represented in simpleFoam. Maybe I miss sth? Or this omission can not be applied in unstaggered mesh with Rhiechow interpolation? Because from Hrv's thesis, the math model behind simpleFoam is quite clear and straightforward. Best,
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June 15, 2015, 04:13 

#2 
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Hiroaki Fujio
Join Date: Aug 2013
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Hi,
The algorithm of simpleFoam looks different from what is refered to as SIMPLE algorithm by many of us. In SIMPLE algorithm, U* is calculated from the momentum equation and then p' is calculated by substituting U* to the continuous equation. But simpleFoam calculates HbyA (which is identical to U^ of SIMPLER algorithm) instead of U* and then calculates p directly from the continuous equation by substituting HbyA. That is why simpleFoam doesn't have p' and U'. In simpleFoam, U is calculated from U = HbyA  grad(p)/UEqn.A() against U = U* + U' = U*  grad(p')/UEqn.A() of usual SIMPLE algorithm. 

June 15, 2015, 04:21 

#3  
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Dongyue Li
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Quote:
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Im the translator of OpenFOAM User Guide Chinese Edition! But always newbie on CFD. Never too old to learn CFD. Worship these CFD experts. 

June 15, 2015, 04:37 

#4  
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Hiroaki Fujio
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Quote:
SIMPLER algorithm is as follows: 1. Calculate U^ from the momentum equation HbyA = UEqn().H()/UEqn.A() 2. Calculate p from the continuity equation and U^ 3. Calculate Ustar from p calculated in Step 2 U* = HbyA  grad(p)/UEqn.A() ==== simpleFoam ends here and return to Step 1 with U = U* ==== 4. Calculate p' from the continuity equation and U* 5. Correct U using p' but do not correct p U = U*  grad(p')/UEqn.A() 6. Return to Step 1 

June 17, 2015, 18:24 

#5 
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Hiroaki Fujio
Join Date: Aug 2013
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I have to make some corrections.
I misunderstood SIMPLER algorithm. In Step 1, simpleFoam solves momentum equation before calculating HbyA, but SIMPLER calculates U^ from guessed velocity field and doesn't solve momentum equation here. And in Step 3, simpleFoam adds grad(p)/UEqn.A() to HbyA for U, but SIMPLER solves momentum equation here in order to acquire Ustar. And I have to correct the answer to your first question. The spirit of SIMPLE algorithm can be seen in the pressure equation of simpleFoam. By applying the approximation of H(U') = 0, U can be expressed as U = H(U*)/A  grad(p)/A. Therefore div(U) = div(H(U*)/A)  laplacian(1/A, p) = 0, which is identical to pEqn. So simpleFoam is on SIMPLE algorithm. I was wrong. I am sorry for misleading you. 

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