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New implementation of Courant number in version 2.0 |
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August 17, 2011, 04:02 |
New implementation of Courant number in version 2.0
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#1 |
Senior Member
Steven van Haren
Join Date: Aug 2010
Location: The Netherlands
Posts: 149
Rep Power: 15 |
Dear All,
There seems to be a new implementation of the Courant number in version 2.0.x (compared to 1.7.1). The Courant number seems to be calculated cell-based instead of face-based. To me this seems strange since high velocity peaks will be smeared over a cell. Also there seems to be a mysterious 0.5 factor. Does anybody has some useful thoughts about why they changed this for version 2.0? Any input will be greatly appreciated. |
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August 18, 2011, 04:23 |
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#2 |
Senior Member
Eugene de Villiers
Join Date: Mar 2009
Posts: 725
Rep Power: 21 |
The "0.5" can what is going on can be easily explained. The "sumPhi" scalar field represents the magnitude of the volume flux crossing crossing a cell boundary. Since the amount of flux out must be equal to the amount of flux in to satisfy continuity, the "average" flux magnitude must be exactly 0.5*sumPhi.
No consider an arbitrary cell in a uni-directional flow field. The cell will have some equivalent frontal area, A*, normal to the flow direction. It will also have some equivalent average length d* aligned with the flow direction. (It follows that V (volume) = A* x d*.) The Courant number is defined as CFL = velocity * dt / length. Using the average flux magnitude, you can show that CFL = (0.5 sumPhi / A* ) x dt / d* = 0.5 sumPhi x dt / V As to why this was done, I have no idea. As you mentioned, the above formulation will obviously be less accurate the more curved the flow is. |
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August 18, 2011, 05:25 |
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#3 |
Senior Member
Steven van Haren
Join Date: Aug 2010
Location: The Netherlands
Posts: 149
Rep Power: 15 |
Thank you for your explanation, the 0.5 factor is clear to me know.
If anybody has an idea why this was done I would be very interested. Kind regards, Steven |
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