# The spirit of SIMPLE algorithm in simpleFoam

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May 30, 2015, 11:21
The spirit of SIMPLE algorithm in simpleFoam
#1
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Dongyue Li
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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 un-staggered mesh with Rhie-chow 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 New Member   Hiroaki Fujio Join Date: Aug 2013 Posts: 3 Rep Power: 3 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:
 Originally Posted by Conte 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.
So maybe simpleFoam is simpleR algorithm with Rhie-chow interpolation? No wonder why there is not simpleR in openfoam and flunet....
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June 15, 2015, 04:37
#4
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Hiroaki Fujio
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Quote:
 Originally Posted by sharonyue So maybe simpleFoam is simpleR algorithm with Rhie-chow interpolation? No wonder why there is not simpleR in openfoam and flunet....
No, simpleFoam is different from SIMPLER as well.

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

==== 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

 June 17, 2015, 18:24 #5 New Member   Hiroaki Fujio Join Date: Aug 2013 Posts: 3 Rep Power: 3 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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