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Taylor-Green vortex sheet

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Old   March 29, 2016, 05:29
Default Taylor-Green vortex sheet
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Daniel Duque
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Hello,

I have been simulating the Taylor-Green vortex sheet with OpenFOAM. My main target is to establish how the error decreases with the time-step Dt, for fixed Courant number. I am guessing it should be proporcional to Dt^2, as shown in this Example.

However, I am getting this puzzling result


It seems to show a very rapid decay, as Dt^4 for longer times, but then the error stalls completely. I thought it may have to do with the precision used to write the results (I have had those issues in the past), but increasing the number of decimals does not change much.

I would really appreciate if anyone has an explanation for this. It could be that the method does not improve below some spacial resolution? I am really interested in this because I am implementing a new CFD particle method, and it would be great to compare it against OpenFOAM.

I am uploading a run directory for the second smallest time-step. The rest can be easily re-created by doubling the time-step in controlDict and the cell size in blockMeshDict (or the opposite). Notice I am running at Re=200, and Co=0.5, at variance with the example quoted above. The python utility I have written to obtain the error is also included. The final error lacks a sqrt, which is included in the figure above.
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