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Limits of SIMPLE algorithm

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Old   June 10, 2009, 04:13
Default Limits of SIMPLE algorithm
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Fernando Herrera
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Hi,

I was wondering if someone knows the limits of the SIMPLE algorithm.

What is the maximum speed that it can work with?
Is it limited by the Reynolds number?

I'm asking these questions because of my code. I've developed a small code that calculates the flow field in 2D. But, I've noticed that if the entry speed is high, the code goes bananas. Now my code is stable with entry speeds below 2 m/s and density of 1.

I haven't found a proper reason for this. I've been reading the books by Versteeg and Anderson, but I cannot find something that I can use to justify the behavior.

Please, I will appreciate any help, or the name of a book that I could read.
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Old   June 10, 2009, 11:42
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SIMPLE is pretty terrible for many purposes. A more general approach which contains SIMPLE as a special case are preconditioners based on block factorization. For example,

Code:
@article{elman2008tcp,
  title={{A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations}},
  author={Elman, H.C. and Howle, V.E. and Shadid, J. and Shuttleworth, R. and Tuminaro, R.},
  journal={Journal of Computational Physics},
  volume={227},
  number={1},
  pages={1790--1808},
  year={2008},
  publisher={Academic Press}
}
or the comprehensive

Code:
@article{benzi2005nss,
  title={{Numerical solution of saddle point problems}},
  author={Benzi, M. and Golub, G.H. and Liesen, J.},
  journal={Acta Numerica},
  volume={14},
  pages={1--137},
  year={2005},
  publisher={Cambridge Univ Press}
}
If you are concerned about efficiency with small subdomains on massively parallel archituctures, you may want to look at Vanka smoothers for multigrid or multilevel domain decomposition that respects indefiniteness, but the block preconditioners in Elman's paper provide an excellent framework for robust solvers and they have been shown to scale nearly linearly to 65k processes and 40B degrees of freedom.
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