open TELEMAC-MASCARET The mathematically superior suite of solvers

Hi,

I would like to know if there is some theorical notions to choose time steps. I took a look to examples of TOMAWAC and time step can vary from 0.3 to 1000s something like that.
My model has a space hold about 60 km * 40 km. The meshes go from 500m to 10m. I must take into account depth-induced breaking.
Until now, I have chosen a time step of 5s and 3 iterations for source terms. The difference between the breaking models is huge. I thought it could be linked to time step.

Thank you very much for your help,
Pauline

Hi,
As rule of thumb, you should set the time step in order to have a Courant number between 1 ad 2.
The Courant number Cr is given by : Cr=C_g(f_p)*Dt//Dx
Where C_g(f_p)is the group velocity associated to the peak frequency, Dt is the time step and Dx is the size of the smallest element of the spatial mesh.
The group velocity can be calculated from the dispersion relation. In the deep water case, the group velocity is approximately equal to 0.78/f_p, while in shallow waters C_g=(g*d)^0.5, where g is the gravity acceleration and d is the water depth.

Hope it helps,

Giovanni

Thank you very much for that clear and precise answer.

I have another question. It is the second time you get onto "rule of thumb". Could you tell us more about this ? Would you have documents about it ?

Thank you very much anyway,

Kind regards,
Pauline

Rule of thumb = point de repère, régle générale
www.larousse.fr/dictionnaires/anglais-francais/rule/608684

Kind regards,

Giovanni

Or "méthode empirique" in French
www.oqlf.gouv.qc.ca/ressources/gdt.html

Regards,

Chi-Tuan

Thank you, sorry for that...

Hi everyone

After reading this topic, I have 2 more questions:

1. Is there any mistakes in my calculation below?

The Courant number Cr is given by : Cr=Cg(fp)*Dt//Dx

Cg(fp)is the group velocity associated to the peak frequency = 0.78/0.1 =7.8 (fp = 1/T = 1/10 = 0.1)

Dx is the size of the smallest element of the spatial mesh = 150m

----> Dt= 150/7.8 = ~ 19 (Cr=1) and Dt = 2x150/7.8 = 40 (Cr=2)

So, In sum up, Dt ranges from 20s t0 40s

2. I saw in examples directory of TOMAWAC, and some cases on this forum, a time step of 1200s has been selected. How can they obtain this time-step? it is too large, but I also apply this in my model, it apparently works.



Best Regards

Huy