Courant Number

oliveira1820 · December 6, 2018, 03:09

I know that Courant number should be near 1 to calculate a viable solution, but even with a 999 Courant number, my smulation converges.

Should I work with Courant numbers near 1, which will imply a timestep 1000 smaller, or if the solutton converges, it doesn't matter?

Best regards!

urosgrivc · December 6, 2018, 04:21

it depends on the case if it is ok or not.
it doesn't need to be 1
Mosty depends on vhat phisics you are simulating
Your solution must be timestep size independent,
try different timestep sizes and check your results if these are very different than something is not ok and the solution is not independent.

And courant number as it is, has to be understood properly, what I mean is, let say you want this number to be 1 well then you can either decrease the timestep or aparently increase the mesh size, the coarser the mesh the lower the courant number, but is this a solution or just a unimportant idea? well, that is up to the user to decide...
https://www.sharcnet.ca/Software/Ans.../i1313549.html
https://www.sharcnet.ca/Software/Ans...fxBasiVariCour

ghorrocks · December 6, 2018, 04:40

The Courant number 1 criteria is a hard limit for explicit solvers. If you exceed this the solver will diverged, guaranteed. But it is a common mistake to think this criteria also applies for implicit solvers like CFX. This is why you have got convergence at high Courant numbers, Courant number is not a criteria of much significance for implicit solvers.

You really should ignore the Courant number for CFX. The way to determine time step size for implicit solvers like CFX is to do a sensitivity analysis on the time step size.

oliveira1820 · December 7, 2018, 03:09

Thank you so much for your replys, they were both very helpful.

December 6, 2018, 03:09	Courant Number	#1
oliveira1820 Senior Member Pedro Oliveira Join Date: Feb 2018 Location: Portugal Posts: 109 Rep Power: 8	I know that Courant number should be near 1 to calculate a viable solution, but even with a 999 Courant number, my smulation converges. Should I work with Courant numbers near 1, which will imply a timestep 1000 smaller, or if the solutton converges, it doesn't matter? Best regards!

December 6, 2018, 04:21		#2
urosgrivc Senior Member urosgrivc Join Date: Dec 2015 Location: Slovenija Posts: 365 Rep Power: 11	it depends on the case if it is ok or not. it doesn't need to be 1 Mosty depends on vhat phisics you are simulating Your solution must be timestep size independent, try different timestep sizes and check your results if these are very different than something is not ok and the solution is not independent. And courant number as it is, has to be understood properly, what I mean is, let say you want this number to be 1 well then you can either decrease the timestep or aparently increase the mesh size, the coarser the mesh the lower the courant number, but is this a solution or just a unimportant idea? well, that is up to the user to decide... https://www.sharcnet.ca/Software/Ans.../i1313549.html https://www.sharcnet.ca/Software/Ans...fxBasiVariCour Last edited by urosgrivc; December 6, 2018 at 05:52.

December 6, 2018, 04:40		#3
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,700 Rep Power: 143	The Courant number 1 criteria is a hard limit for explicit solvers. If you exceed this the solver will diverged, guaranteed. But it is a common mistake to think this criteria also applies for implicit solvers like CFX. This is why you have got convergence at high Courant numbers, Courant number is not a criteria of much significance for implicit solvers. You really should ignore the Courant number for CFX. The way to determine time step size for implicit solvers like CFX is to do a sensitivity analysis on the time step size. Yagu94 likes this. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

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December 7, 2018, 03:09		#4
oliveira1820 Senior Member Pedro Oliveira Join Date: Feb 2018 Location: Portugal Posts: 109 Rep Power: 8	Thank you so much for your replys, they were both very helpful.