# Courant number infinity

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 June 17, 2021, 22:04 Courant number infinity #1 New Member   Join Date: Jun 2021 Posts: 3 Rep Power: 4 Hello Everyone! What could be the reasons/causes why the Courant number is infinity? In pratice, what steps do you suggest to do in order to fix this issue? Thanks!

 June 18, 2021, 06:45 #2 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,120 Blog Entries: 29 Rep Power: 38 The courant number can be roughly defined as U dt/dx. Thus, generally speaking, as long as you used a mesh with cells of finite dimension dx and a finite time step dt, the only reason for an infinite courant number is the divergence of the field U. This is the best one can say without any further information. aero_head likes this.

 June 18, 2021, 09:53 #3 New Member   Join Date: Jun 2021 Posts: 3 Rep Power: 4 Thank you for the reply! I am trying to debug my simulations since I get a courant number of infinity, but the time step is finite, and the cells have finite dimensions too. So I guess the problem is the divergence of U.

June 18, 2021, 09:56
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Paolo Lampitella
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Quote:
 Originally Posted by Gualti Thank you for the reply! I am trying to debug my simulations since I get a courant number of infinity, but the time step is finite, and the cells have finite dimensions too. So I guess the problem is the divergence of U.
Well, it is indeed strange that you did notice an infinite value for CFL but not for your solved variable, the velocity (that's what I meant for divergence, which now occurs to me might have been an unhappy choice of terms).

 June 23, 2021, 15:33 #5 New Member   Join Date: Jun 2021 Posts: 3 Rep Power: 4 Thanks. May I ask how can I check that the elements of the mesh have a finite dimensions? I am using GMSH, and it provides the gamma value (ratio between inscribed radius and circumscribed radius). This value ranges between 0.2 and 1 in my mesh. Is it enough to say that the elements have a finite dimension? I am trying to improve the mesh, and in some cases I also get Courant number of -1, but I can't explain why. Thank you!

 June 23, 2021, 15:54 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,597 Rep Power: 70 First of all, what is the software? Are you aware about the way the CFL is computed? Check that all volumes are positive quantities. However, you could simply experiencing a numerical instability, what about the velocity field? sbaffini likes this.

June 24, 2021, 03:57
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Paolo Lampitella
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Quote:
 Originally Posted by Gualti Thanks. May I ask how can I check that the elements of the mesh have a finite dimensions? I am using GMSH, and it provides the gamma value (ratio between inscribed radius and circumscribed radius). This value ranges between 0.2 and 1 in my mesh. Is it enough to say that the elements have a finite dimension? I am trying to improve the mesh, and in some cases I also get Courant number of -1, but I can't explain why. Thank you!
Courant = -1 Sounds like a mesh problem. But you need to check the manual of the software you are using to know how their courant is computed. The same for the gamma in gmsh (which, however, I understand lower is better)

 Tags courant number, mesh 3d