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Comparison of different spatial and temporal discretization schemes

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Old   March 17, 2009, 23:37
Default Comparison of different spatial and temporal discretization schemes
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Daniel Harlacher
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Hey,

I am studying the behaviour of vortex shedding behind a cylinder/sphere and now I want to see how different discretization methods influence the resulting von Kármán street.

I worked with various other solver before in which one could define the order of the spatial and temporal discretisation in a fairly simple manner. But concerning OpenFOAM it seems one has a lot more choice to influence the behaviour of the solver.

I read both programmers ans users guide and decided, that the two important "schemes" to play around would be the timeScheme (of course) and the convection scheme (div).

That still leaves me with a lot of choices - which I am not capable of comparing all - so I would like to strip it down to useful comparisons.

Do you have any ideas or maybe even experience with the different schemes, then I would be happy to know about that. Something I never came across before is the property of "bounded" and "unbounded", maybe somebody could help me out with this?

Once I have decided on a test setup I will post the relevant data and results in this thread.

I will probably be starting with a square cylinder - as I have the grid and reference results for that one.

Yours
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Old   March 18, 2009, 02:38
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Alberto Passalacqua
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Hi,

for the time discretization:
  • Euler is first order accurate
  • Crank-Nicholson and backward are second order accurate
For the divergence term:
  • linear corresponds to second order central differences.
  • limitedLinear and limitedLinearV are the limited version of the linear scheme, so their accuracy is reduced when the limiter kicks in.
  • cubicCorrected should be a fourth order central difference scheme.
You can find some additional information in the user's manual, page 112, table 4.10.

For your case, as a starting point, you might try the backward scheme for time integration and the linear scheme for the convective term.

I hope this helps.
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Old   September 24, 2011, 12:15
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Quote:
Originally Posted by alberto View Post
Hi,

for the time discretization:
  • Euler is first order accurate
  • Crank-Nicholson and backward are second order accurate
For the divergence term:
  • linear corresponds to second order central differences.
  • limitedLinear and limitedLinearV are the limited version of the linear scheme, so their accuracy is reduced when the limiter kicks in.
  • cubicCorrected should be a fourth order central difference scheme.
You can find some additional information in the user's manual, page 112, table 4.10.

For your case, as a starting point, you might try the backward scheme for time integration and the linear scheme for the convective term.

I hope this helps.
Dear Alberto,

Has any three-level method for temporal discretization been developed so far? I couldn't find it in either manual or src folder; it seems that many changes need because of using previous time step data for that, right?
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