# 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 #1 Senior Member   Steven van Haren Join Date: Aug 2010 Location: The Netherlands Posts: 149 Rep Power: 9 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.

 August 18, 2011, 04:23 #2 Senior Member   Eugene de Villiers Join Date: Mar 2009 Posts: 725 Rep Power: 14 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.

 August 18, 2011, 05:25 #3 Senior Member   Steven van Haren Join Date: Aug 2010 Location: The Netherlands Posts: 149 Rep Power: 9 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

 August 18, 2011, 05:26 #4 Senior Member   Laurence R. McGlashan Join Date: Mar 2009 Posts: 370 Rep Power: 16 You could always ask them! __________________ Laurence R. McGlashan :: Website

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