# double-projection method that works on non-staggered grid

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February 11, 2017, 16:27
double-projection method that works on non-staggered grid
#1
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Bernd
Join Date: Jul 2012
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This is a follow up to a branch of another thread (i thought to open a new thread in order to not 'hijack' th other thread that originally had another topic)

In that thread we discussed Approximate Projection Methods (APM) and FMDenaro wrote:

Quote:
 Originally Posted by FMDenaro Thus, I developed an exact double-projection method that works on non-staggered grid. I had good and oscillation-free solutions without adding dissipation. F
This double-projection method sounds very interesting indeed.

I have one question: Am I correct to assume that for the second elliptic solve of the "double projection" one can get away with significantly fewer iterations of the linear solver to reach the error tolerance ?

This would be important for the practicality of the method because typically already the first regular "single projection" solve takes most of the time of the whole simulation step.

But if it would be possible to solve the 'second stage' of your double projection method with, say, only a limited number of additional gauss-seidel/jacobi sweeps or Conjugate-Gradient iterations then this would be a very interesting option to consider to improve my non-staggered approximate pressure correction method.

February 11, 2017, 19:40
#2
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,817
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Quote:
 Originally Posted by zx-81 This is a follow up to a branch of another thread (i thought to open a new thread in order to not 'hijack' th other thread that originally had another topic) In that thread we discussed Approximate Projection Methods (APM) and FMDenaro wrote: This double-projection method sounds very interesting indeed. I have one question: Am I correct to assume that for the second elliptic solve of the "double projection" one can get away with significantly fewer iterations of the linear solver to reach the error tolerance ? This would be important for the practicality of the method because typically already the first regular "single projection" solve takes most of the time of the whole simulation step. But if it would be possible to solve the 'second stage' of your double projection method with, say, only a limited number of additional gauss-seidel/jacobi sweeps or Conjugate-Gradient iterations then this would be a very interesting option to consider to improve my non-staggered approximate pressure correction method.
Yes, the second elliptic equation requires much less iteration to reach convergence, if you found my papers on IJNMF that is clarified ...
Of course, I used to start the iterations from the solution of the previous time step

February 12, 2017, 04:10
#3
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Bernd
Join Date: Jul 2012
Posts: 42
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Quote:
 Originally Posted by FMDenaro Yes, the second elliptic equation requires much less iteration to reach convergence, if you found my papers on IJNMF that is clarified ... Of course, I used to start the iterations from the solution of the previous time step
Thanks a lot for the clarification !
I will try to digest the papers to better understand the details of the method.

 February 12, 2017, 04:23 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,817 Rep Power: 73 Ok, if you have questions you can ask for infos. The links of the two papers: https://www.researchgate.net/publica...y-driven_flows https://www.researchgate.net/publica...ids?ev=prf_pub but I think that to understand better the theoretical basis of the DPM the details are here in this third paper https://www.researchgate.net/publica...ary_conditions