open TELEMAC-MASCARET The mathematically superior suite of solvers

I would like to know the influence of desired current number in a simulation.

For me current number = speed * time step / mesh size. Mesh size is fixed during a run. The speed should not be changed be this parameter so current number change time step. I'm not sure if it's true?

Then which kind of value (minimum and maximum) is acceptable for the desired current number? I just know that the default value is 1.

To finish, when a simulation is running the maximum current number appears two times in the console :
PRERES : NOMBRE DE COURANT MAXIMUM : 0.5001970
NOMBRE DE COURANT MAXIMUM : 0.5001970
I have some simulation where the two values are not the same. What is the difference between the two values?

Thank you in advance

Regards

Hello,

Actually it is not the current number, it is the Courant number, Mr. Courant being a colleague of Friedrich and Levy, hence the CFL number. Telemac is not very sensitive to it, and a value around 1 is OK. Depending on what you do, it is U*DT/DX or (U+C)*DT/DX, C the celerity of waves. For advection terms it is U*DT/DX. This is in 1D and in 2D the DX is more complicated to evaluate, it depends on the direction. The average value taken in PRERES is different from what is precisely computed for the distributive schemes stability criterion, this is why you may have different values in the listing.

With best regards,

Jean-Michel Hervouet

Hello,

Thank you for your answer.

Sorry for the mistake Courant - current I didn't know it was a name.
I have used the values 3, 1 and 0.5 in my simulation and I note somme difference in stability of free surface so I think than Telemac is sensitive to it.
When you say around 1, can you be more precise (0.9 to 1.1 or 0.1 to 10)?
Ok for PRERES.

Regards

Hello,

Yes I mean that there is no stability problems as other explicit programs that will crash if the Courant number trespasses 1. The results may be slightly different as the error is first order in DT. Then it is difficult to give a precise number, especially if the mesh size is varying. For example the method of characteristics in 1D on a regular grid is exact with Courant numbers equal to 1, 2, 3, etc. If you use too small time steps, you will get more numerical diffusion and truncation errors will accumulate, so I'll say that for Telemac 0.1 to 2 should be OK, but actually I often look at the number of iterations of the propagation step, which says if the problem is hard or not. From 1 to 20 iterations of conjugate gradient is OK.

With best regards,

Jean-Michel Hervouet

Ok it's clearer for me now. Thank you

Regards

Hi,
My mesh size is 4, velocity is 0.6 and if I use time step 0.01, then courant number becomes 0.0015, which is very low. If I try to increase the courant number and keep is closer to 1 then my time step needs to be 2. But in this simulation, time step 2 doesn't work and 0.01 works very well. I know courant number less than 1 is good, but in my case, it is less than 1 and a very low number. Is there a minimum value for courant number? How a low courant value can affect the simulation accuracy? Thanks.

Using such a low courant number is not typical. Perhaps your model has instabilities during the first few timesteps due to the initial conditions being too far away from reality.

In cases where I see large initial courant numbers which quickly reduce over subsequent timesteps I sometimes use a computation continued approach with a low timestep for the initial spinup and then switch to a larger timestep one the initial conditions are better specified. This is mostly to reduce the computational time though.