Courant number infinity
 

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!

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.

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).

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!

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?

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)